UPTEC ES 19023
Examensarbete 30 hp Augusti 2019
Case Study of Photovoltaics and Electric Vehicle Charging
in a Low-Voltage Distribution Grid
Anton Gustafsson
Teknisk- naturvetenskaplig fakultet UTH-enheten
Besöksadress:
Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0
Postadress:
Box 536 751 21 Uppsala
Telefon:
018 – 471 30 03
Telefax:
018 – 471 30 00
Hemsida:
http://www.teknat.uu.se/student
Abstract
Case Study of Photovoltaics and Electric Vehicle Charging in a Low-Voltage Distribution Grid
Anton Gustafsson
This thesis investigates the effects from a grid connection of photovoltaics and electric vehicle charging in a low-voltage distribution grid. The study has taken place on behalf of Norrtälje Energi AB, and the object of study is a customer in one of their rural grids. Due to reported disturbances by the customer, a Magtech Voltage Booster (MVB) was installed at the point of common coupling.
To evaluate the situation, three power quality measurements were analysed. Furthermore, a model of the distribution grid was developed in OpenDSS.
The main conclusion of this thesis is that the disturbances seems to be caused by temporary voltage drops (below 195.5 V) during charging hours. This situation continues to create problems even though the MVB boosts and balances the voltage. The power quality measurements showed that the voltage unbalance, during charging hours, violated the limit both before and after the MVB-installation. Another significant conclusion in this thesis is that the MVB does not seem to improve the power quality, on the contrary it deteriorates the power quality with regards to rapid voltage change and harmonic content. Furthermore, the OpenDSS-model was able to predict the temporary voltage drops. And the model also resulted in voltage unbalance comparable to the measurements. The model also displayed how the voltage unbalance and harmonic content mitigated to other parts of the grid, and it became clear that it is only the closest neighbour that is in the risk of deteriorated power quality.
ISSN: 1650-8300, UPTEC ES19 023 Examinator: Petra Jönsson
Ämnesgranskare: Juan de Santiago Handledare: Annette Wikström
Popul¨ arvetenskaplig sammanfattning
F¨or att uppn˚a Sveriges klimatpolitiska m˚al kr¨avs en teknisk omst¨allning i samh¨allet. De senaste ˚aren har f¨orekomsten av elbilar och solcellsanl¨aggningar ¨okat markant i Sverige.
Fr˚an 1200 laddningsbara bilar ˚ar 2012 till 69 000 ˚ar 2018. Enligt branchorganisationen Power Circle, f¨orutsp˚as 2 500 000 laddningsbara bilar i Sverige till ˚ar 2030. En liknande trend kan ses f¨or solcellsanl¨aggningar. Den totala installerade effekten av n¨atanslutna solcellsanl¨aggningar ¨ar 180 g˚anger h¨ogre ˚ar 2017 j¨amf¨ort med 2007. Priset sjunker ocks˚a kraftigt, fr˚an 63,3 SEK/Wp˚ar 2010 till 14,8 SEK/Wp 2017 (exklusive moms).
Detta examensarbete unders¨oker hur eln¨atet p˚averkas av en anslutning med elbilsladdning och solcellsanl¨aggning. Arbetet kretsar kring en kund i Norrt¨alje Energis eln¨at, kunden
¨ar ansluten med en solcellsanl¨aggning och har en elbil. Projektet tar avstamp i inrappor- tering av st¨orningar p˚a att solcellsanl¨aggningen kopplar ur. Norrt¨alje Energi har f¨or att
˚atg¨arda detta problem installerat en Magtech Voltage Booster (MVB), vars uppgift ¨ar att balansera och reglera upp sp¨anningen i n¨atet. M˚alet med detta arbete ¨ar att utreda elkva- litetsm¨atningar som har gjorts vid anslutningen, utv¨ardera inverkan av Magtech voltage booster, samt att unders¨oka om st¨orningarna hade kunnat f¨orutsp˚as. ¨Aven alterna- tiv f¨or att f¨orb¨attra elkvaliten unders¨oks, som n¨atf¨orst¨arkning och Ferroamps EnergyHub.
Tre stycken elkvalitetsm¨atningar analyserades f¨or att bed¨oma elkvaliten och f¨or att utv¨ardera MVB:n. Elkvalitetsm¨atningarna utf¨ordes med Metrum SPQ, och resultatet bed¨omdes utifr˚an Energimarknadsinspektionens normer. Tv˚a av m¨atningarna, en f¨ore installationen av MVB:n och en efter installationen, ¨ar utf¨orda av Norrt¨alje Energi AB vid kundens m¨atarsk˚ap. En tredje m¨atning utf¨ordes som en del av detta arbete vid solcellsanl¨aggningens v¨axelriktare. En modell utformades i programmet OpenDSS, baserat p˚a data fr˚an Trimble NIS, f¨or distributionsn¨atet i fr˚aga. Syftet med modellen var att unders¨oka om st¨orningarna hade kunnat f¨orutsp˚as, samt att unders¨oka hur elkvaliten p˚averkas i andra delar av n¨atet. OpenDSS-modellen simulerades med olika scenarion och inst¨allningar f¨or att utv¨ardera situationen.
Fr˚an den f¨orsta elkvalitetsm¨atningen, utf¨ord innan installation av MVB:n, kan det ses att m¨atningen blev underk¨and p˚a l˚angsam undersp¨anning och sp¨anningsobalans. Fr˚an elkva- litetsm¨atningen kan det ses att sp¨anningen sjunker kraftigt p˚a den fas som elbilen laddar p˚a under laddning. ¨Aven sp¨anningsobalans uppst˚ar vid kraftigt obalanserad last. Efter installationen av MVB:n s˚a kunde det utl¨asas av elkvalitetsm¨atningen att sp¨anningen var mer balanserad mellan faserna, ¨aven vid obalanserad last, samt att sp¨anningen hade en generellt h¨ogre magnitud. Trots detta blev m¨atningen underk¨and p˚a sp¨anningsobalans, snabba sp¨annings¨andringar och individuella ¨overtoner. ¨Aven m¨atningen vid v¨axelriktaren blev underk¨and p˚a sp¨anningsobalans, snabba sp¨annings¨andringar och individuella
¨overtoner. Vid v¨axelriktaren uppstod en markant skillnad i magnitud mellan faserna vid laddning.
Fr˚an simuleringarna av modellen i OpenDSS stod det klart att de kraftiga sp¨anningss¨ankningarna, som f¨ormodar vara orsaken till fr˚ankopplingen, kunde f¨orutsp˚as.
Dessutom resulterade modellen i en liknande situation f¨or sp¨anningsobalans. Det kunde
¨aven ses att sp¨anningsobalansen var relativt h¨og vid n¨armsta granne, vilket antyder att h¨og sp¨anningsobalans kan f¨orekomma hos grannen i verkligheten. Fr˚an ¨overtonsanalysen
kunde det klarg¨oras hur mycket sp¨annings¨overtoner avtar i n¨atet. N¨ar modellen simule- rades med n¨atf¨orst¨arkningar kunde det ses att sp¨anningen ¨okade lite i magnitud, men inte tillr¨ackligt mycket f¨or att kunna vara ett rimligt alternativ till MVB:n. Det kunde dock ses att n¨atf¨orst¨arkningen s¨ankte sp¨anningsobalansen. Den st¨orsta skillnaden som n¨atf¨orst¨arkningen bidrog till var en l¨agre ¨overtonshalt.
En av de viktigaste slutsatserna fr˚an detta arbete ¨ar att MVB:n, trots sp¨anningsreglering, inte tycks h¨oja de tillf¨alliga sp¨anningsfallen vid v¨axelriktaren tillr¨ackligt mycket f¨or att undvika fr˚ankoppling vid laddning. MVB:n tycks ¨aven f¨orv¨arra ¨overtonshalten. Trots detta f¨orb¨attrar installationen av MVB:n sp¨anningsniv˚an vid anslutningspunkten, vilket
¨ar Norrt¨alje Energis ansvar som n¨at¨agare.
Exekutiv sammanfattning
Detta examensarbete unders¨oker elkvaliten vid en kund som ¨ar ansluten till n¨atet med en solcellsanl¨aggning. Kunden har ¨aven en elbil, och har rapporterat in att solcellsanl¨aggningen kopplar ur vid elbilsladdning. Norrt¨alje Energi har installerat en Magtech Voltage Booster (MVB) f¨or att st¨avja problemet. Efter installationen av MVB:n visar elkvalitetsm¨atningarna en tydlig sp¨annings¨okning. Trots detta visar elkva- litetsm¨atningar vid solcellsanl¨aggningen att tempor¨ara sp¨anningsfall, som understiger 195.5 V och d¨armed trippar utrustningen, kvarst˚ar vid laddningstillf¨allena. Det ¨ar dessa undersp¨anningar som antas vara orsaken till det kvarst˚aende problemet av urkoppling av solcellsanl¨aggninen. Dock visar elkvalitetsm¨atningarna att MVB:n h¨ojer, och d¨armed f¨orb¨attrar, sp¨anningen vid Norrt¨alje Energis avl¨amningspunkt. Elkvalitetsm¨atningarna visar ocks˚a att sp¨anningsobalansen inte f¨orb¨attras av MVB:n, samt att ¨overtonshalten tycks vara h¨ogre med MVB:n i n¨atet. Antalet snabba sp¨annings¨andringar ¨okar efter implementeringen av MVB:n och ¨overstiger vid flertalet g˚anger gr¨ansen fr˚an Energimark- nadsinspektionens normer.
En modell uppr¨attades i OpenDSS, baserat p˚a data fr˚an Trimble NIS, med syftet att unders¨oka om st¨orningarna hade kunnat f¨orutsp˚atts och f¨or att unders¨oka situatio- nen i ¨ovriga delar av n¨atet. De tillf¨alliga sp¨anningsfallen under 195.5 V vid laddning kunde f¨orutsp˚as med hj¨alp av modellen. Modellen resulterade ¨aven i en likv¨ard mag- nitud av sp¨anningsobalans. Fr˚an modellen kunde det ses att sp¨anningsobalansen och
¨overtonshalten kraftigt avtog h¨ogre upp i n¨atet, d¨ar flera andra kunder ¨ar anslutna. En- dast vid den n¨armsta grannen kan det ses en m¨arkbar f¨ors¨amring av elkvaliten. Vidare visade det sig att n¨atf¨orst¨arkning hade en m¨arkbar f¨orb¨attring f¨or sp¨anningsobalans och
¨overtonshalt.
Acknowledgements
This thesis completes my studies at the master’s programme in Energy Systems Engi- neering at Uppsala University and the Swedish University of Agricultural Sciences. The thesis covers 30 credits and has been conducted on behalf of Norrt¨alje Energi AB during the spring semester of 2019.
I would like to show my gratitude towards Norrt¨alje Energi AB for giving me the op- portunity to complete an interesting thesis. A special thanks to my supervisor, Annette Wikstr¨om, for support and guidance throughout the project. I would also like to thank Juan de Santiago at the Division of Electricity at Uppsala University for helpful discus- sions.
Anton Gustafsson Uppsala, June 2019
List of symbols and abbreviations
Symbols
U Voltage [V]
I Current [A]
ϕ Phase angle [°]
Z Impedance [Ω]
R Resistance [Ω]
X Reactance [Ω]
B Susceptance [S]
S Complex power [VA]
P Active power [W]
Q Reactive power [var]
T HD Total harmonic distortion [%]
Abbreviations
RMS Root mean square LV Low voltage MV Medium voltage
PCC Point of common coupling p.u. Per unit
RVC Rapid voltage change PV Photovoltaics
EV Electric vehicle VAT Value added tax
Subscripts
a, b, c, n Phases
0, 1, 2 Sequence components (zero, positive, and negative) h Harmonic order
stat RVC of type stationary (or steady-state) max RVC of type maximum
p Peak power at standard test conditions sc Short circuit
oc Open circuit
mpp Maximum power point
Contents
Popul¨arvetenskaplig sammanfattning i
Exekutiv sammanfattning iii
Acknowledgements iv
List of symbols and abbreviations v
1 Introduction 1
1.1 Problem description . . . 1
1.2 Aim and research questions . . . 2
1.3 Limitations and assumptions . . . 2
1.4 Disposition . . . 3
2 Theory 4 2.1 Electrical grid . . . 4
2.1.1 Distribution grid . . . 4
2.2 Power flow . . . 6
2.3 Harmonics . . . 7
2.4 Power quality . . . 9
2.4.1 Grid codes . . . 9
2.4.1.1 Slow voltage variation . . . 9
2.4.1.2 Voltage unbalance . . . 9
2.4.1.3 Short term voltage drop . . . 10
2.4.1.4 Short term voltage rise . . . 10
2.4.1.5 Rapid voltage change . . . 10
2.4.1.6 Voltage harmonics . . . 11
2.4.2 Guidelines by Energif¨oretagen . . . 11
2.5 Balancing techniques . . . 12
2.5.1 Magtech Voltage Booster . . . 12
2.5.2 Energyhub . . . 13
2.6 Photovoltaics . . . 14
2.6.1 Solar cell . . . 14
2.6.2 PV-system . . . 15
2.7 Electric vehicles . . . 15
3 Method and data 17 3.1 Customer . . . 17
3.2 Power quality measurements . . . 18
3.3 Trimble NIS . . . 19
3.4 OpenDSS . . . 19
3.4.1 Harmonic analysis . . . 22
3.4.2 Validation . . . 23
3.5 Alternative solutions . . . 23
3.5.1 Grid reinforcement . . . 23
3.5.2 Energyhub . . . 24
4 Result 25
4.1 Power quality measurements . . . 25
4.1.1 Prior to the MVB . . . 25
4.1.2 With the MVB in the grid . . . 28
4.1.3 At the inverter . . . 31
4.2 OpenDSS simulation . . . 34
4.2.1 Scenario 1 . . . 35
4.2.2 Scenario 3 . . . 36
4.2.3 Scenario 5 . . . 37
4.2.4 Scenario 7 . . . 38
4.2.5 Summary . . . 38
4.2.6 Harmonic analysis . . . 39
4.3 Alternative solutions . . . 44
4.3.1 Grid reinforcements . . . 44
4.3.2 EnergyHub . . . 45
5 Discussion 47 5.1 Power quality measurement . . . 47
5.2 OpenDSS . . . 48
5.3 Alternative solutions . . . 50
5.4 Further studies . . . 50
6 Conclusions 51
References 53
Appendix A: Loads 54
Appendix B: Validation 55
Appendix C: OpenDSS-simulation 57
List of Figures
1 a) one of the two roofs with photovoltaic modules, b) the location of the
customer. . . 2
2 Schematic structure of the electrical grid. . . 4
3 Distribution grid topologies, (a) double-cable, (b) loop, and (c) radial grid. 5 4 Equivalent circuit of a short transmission line. . . 5
5 Waveform as a result of the fundamental harmonic acting together with the third harmonic. . . 7
6 (a) magtech adjustable inductor [34], (b) single phase equivalent of the MVB [21]. . . 13
7 Adaptive current equalization balancing the currents to an unbalanced load [15]. . . 14
8 (a) circuit equivalent of a solar cell, (b) IV-characteristics for a generic solar cell. . . 15
9 Imported electricity profile for 2018. . . 17
10 Simplified single line diagram of the distribution grid. . . 19
11 Norton equivalent for the harmonic source in OpenDSS. . . 22
12 10-minute values of the voltage and current (in the bottom two panels) together with the minimum voltage in the top panel, for a couple of days in March 2018. . . 27
13 An episode of 10-minute values of voltage unbalance and current for the measurement in March 2018. The dashed purple line represents the EIFS limitation for voltage unbalance. . . 27
14 Maximum magnitude of individual harmonics for the measurement period of March 2018. . . 28
15 10-minute value of the voltage (middle panel) together with the minimum voltage (bottom panel) and maximum voltage (top panel) for the end of June to the beginning of July, after the installation of the MVB. . . 29
16 10-minute value of the current, voltage, and voltage unbalance. The dashed line represents the EIFS limit. . . 30
17 Maximum recorded individual voltage harmonics with the MVB in the grid. 30 18 10-minute value of the voltage (middle panel), together with the maximum noted values (top panel) and minimum noted values (bottom panel). . . 32
19 10-minute values of the voltage unbalance together with the average voltage for a week during the measurement period. . . 32
20 Individual harmonics at the PV-inverter. . . 33
21 Apparent power, average voltage, and voltage THD during the 1st of March 2019. . . 33
22 Magnitudes of individual harmonics at the inverter during the 1st of March 2019. . . 34
23 Individual harmonics for scenario 1. . . 40
24 Individual harmonics for scenario 2. . . 41
25 Individual harmonics for scenario 3. . . 42
26 Individual harmonics for scenario 4. . . 43
27 Individual harmonics for scenario 3, with grid reinforcements. . . 45
List of Tables
1 Regulations for short term voltage drop for systems up to 45 kV. . . 10
2 Guidelines for short term voltage rise for systems up to 1000 V. . . 10
3 Maximum number of allowed rapid voltage changes during 24 hours. . . 10
4 Allowed maximum values for individual harmonics for systems up to 36 kV. 11 5 Protective relay specifications for production units connected to the low- voltage grid [10]. . . 11
6 Guidelines for voltage deviation for PV-systems connected to the grid. . . . 11
7 Guidelines for slow voltage deviation by Energif¨oretagen. . . 12
8 Properties of the PV-system. . . 18
9 Properties for the electrical grid. . . 20
10 Transmission line parameters. . . 21
11 Simulation scenarios for the OpenDSS-model. . . 21
12 Harmonic spectrum for the PV-system at different power outputs [4]. . . . 22
13 Current harmonic content for Nissan Leaf [1]. . . 23
14 Simulation scenarios for the harmonic analysis in OpenDSS. . . 23
15 Long term voltage variations for the power quality measurement in March 2018. . . 25
16 Maximum voltage unbalance for the power quality measurement March 2018. 25 17 Rapid voltage changes for the measured week in 2018. . . 26
18 Number of voltage sags and swells for the measurement period in March 2018. . . 26
19 Maximum measured voltage THD in March 2018. . . 26
20 Rapid voltage changes for one week during the measurement period after the installation of the MVB. . . 31
21 Rapid voltage changes for one week during the measurement period. . . 31
22 Line to neutral phase voltages for scenario 1. . . 35
23 Sequence voltages, together with voltage unbalance, for scenario 1. . . 35
24 Complex phase power for scenario 1. . . 35
25 Line to neutral phase voltages for scenario 3. . . 36
26 Sequence voltages, together with voltage unbalance, for scenario 3. . . 36
27 Complex phase power for scenario 3. . . 36
28 Line to neutral phase voltages for scenario 5. . . 37
29 Sequence voltages, together with voltage unbalance, for scenario 5. . . 37
30 Complex phase power for scenario 5. . . 37
31 Line to neutral phase voltages for scenario 7. . . 38
32 Sequence voltages, together with voltage unbalance, for scenario 7. . . 38
33 Complex phase power for scenario 7. . . 38
34 Summary of voltage of phase A, and voltage unbalance, at the residential connection and at the PV-bus. . . 39
35 Total harmonic voltage distortion (in percentage of fundamental magni- tude) for phase A. . . 39
36 Harmonic content at the transformer, together with the increased eddy- current losses, for scenario 1. . . 40
37 THD at the PV-bus for scenario 1. . . 40
38 Harmonic content at the transformer, together with the increased eddy- current losses, for scenario 2. . . 41
39 THD at the PV-bus for scenario 2. . . 41 40 Harmonic content at the transformer, together with the increased eddy-
current losses, for scenario 3. . . 42 41 THD at the PV-bus for scenario 3. . . 42 42 Harmonic content at the transformer, together with the increased eddy-
current losses, for scenario 4. . . 43 43 THD at the PV-bus for scenario 4. . . 43 44 Line to neutral voltages with implemented grid reinforcements. . . 44 45 Sequence voltages for the model with grid reinforcements, including voltage
unbalance, for scenario 3. . . 44 46 Total harmonic voltage distortion for phase A, for scenario 3, with grid
reinforcements. . . 45 47 Phase voltages and voltage unbalance for the situation with EnergyHub. . 46
1 Introduction
In 2016, a majority of the Swedish parliament agreed on goals regarding energy and cli- mate politics. The agreement includes the goals of no net emissions of greenhouse gases to year 2045, and a completely renewable electricity production to 2030 [28]. Previous to this, in 2012, the Swedish government proposed that Sweden should have a sustainable energy consumption, without net emissions of greenhouse gases, to 2050. A long-term vision of a fossil free vehicle fleet to 2030, is an essential step to fulfil the vision [25].
To reach the objectives, new technologies must be implemented in society. Subsides on photovoltaic-systems and electric vehicles are in practice today, and are incentives for people to invest in the new technologies. The quantity of grid connected PV-systems has been increasing significantly in Sweden the last couple of years. In the last ten years, the installed power of grid-connected systems has increased from a couple of MWp to a total of approximately 300 MWp [20]. The same trend can be seen with chargeable vehicles, where the number of vehicles in traffic has been increasing from 1200 by the end of 2012 to 69 000 at the end of 2018 [27].
The Swedish electrical grid is designed for power flow in one direction, i.e. transmitting power from the high-voltage grid to parts with lower voltage for consumption with mostly linear loads. In the low-voltage distribution grids, the power is assumed to be transmitted from the feeding transformer to the loads downstream. The introduction of the aforemen- tioned new loads and production units, which often utilizes power electronics, is causing problems like unexpected voltage fluctuations, voltage unbalance, and harmonic distor- tion. The impact is especially tangible for weak low-voltage grids, and the impact of the equipment is unique for each distribution grid. To further quantify the problems, and to become better at foreseeing upcoming problems, additional investigations of problematic situations and possible solutions should be made.
1.1 Problem description
A customer in a distribution grid owned by Norrt¨alje Energi AB have reported distur- bances at the connection. The customer, located in a rural distribution grid, owns an electric vehicle and is connected with a 16.4 kWp PV-system. The problem is that the PV-system disconnects when the electric vehicle is charging. A power quality measure- ment was done to evaluate the situation, and it resulted in violation of three power quality indexes: slow voltage variation, voltage unbalance, and voltage sags. The explanation to the problem seems to be that the single-phase charging of the electric vehicle is causing a significant voltage-drop on one phase. To solve the problem, a Magtech Voltage Booster was installed at the point of common coupling. The location of the customer can be seen in figure 1b. The blue lines represents the distribution grid fed by the local distribution transformer, and the yellow lines highlights how the customer (in southeast) is connected to the transformer (in northwest). An 80 m cable has been installed from the residential connection to the location of the EV-charger and the PV-system. Previous power quality measurements were set up at the cable cabinet. To further evaluate the cause of the disturbance one should investigate the power quality at the connection point of the PV and EV.
(a)
(b)
Figure 1: a) one of the two roofs with photovoltaic modules, b) the location of the customer.
1.2 Aim and research questions
The aim of this thesis is to quantify the impact on the rural distribution grid caused by one customer with photovoltaics and an electric vehicle. In the pursuit of doing this power quality measurements are going to be analysed. A model of the situation is also going to be developed in OpenDSS to see if the disturbance could have been predicted.
Furthermore, the thesis aims to evaluate the MVB and to investigate the possibilities of alternative methods for solving the problem. In order to reach the aim, the following research questions are used as an outline:
• How does photovoltaics and charging of an electric vehicle affect the low-voltage distribution grid?
• How does the measured result for an existing system differ from the calculated/pre- dicted case?
• Could the disturbance have been predicted?
• Is there an alternative solution, that would possibly be cheaper, for improved power quality?
1.3 Limitations and assumptions
This study is limited to one specific low-voltage distribution grid. Thus, the results and conclusions in this thesis are not necessarily true for other situations. Furthermore, the technical aspects of the system is the major concern in this study.
1.4 Disposition
Section 2 gives a brief orientation in the subjects covered in this thesis. The power quality norms described in section 2.4.1 are used to evaluate the power quality measurements.
In section 3, the method and information about the equipment and software used in this project are described, together with necessary data. Section 4 covers the results, and is divided into power quality measurements and OpenDSS-simulations. The method and the results are discussed in section 5.
2 Theory
2.1 Electrical grid
The Swedish electrical grid can be divided into three parts: back-bone, regional, and local grid [9]. The back-bone grid is formed by 15 000 km of transmission lines, rated 220 or 400 kV. This part of the grid is transmitting power from large scale production to regional and local grids. The regional grids, rated 20 – 130 kV, are interacting with both production and consumption. Most of the regional grids are owned by E.ON Eln¨at Sverige, Vattenfall Eldistribution, and Ellevio [33]. The regional grids are connected to the local grids. Local grids (also known as distribution grids) are divided into high-voltage and low-voltage parts. The high-voltage part has a nominal voltage above 1 kV, consumers with a high load can be connected to the high-voltage local grid. The low-voltage grid has a nominal voltage less or equal to 1 kV (for AC-power). Most of the electricity customers are connected to the low-voltage part [9]. A schematic structure of the different sections in the Swedish electrical grid can be seen in figure 2.
Back-bone 220 - 400 kV
Regional grid 20 - 130 kV
Distribution grid 10 - 20 kV
Distribution grid 0.4 kV
Figure 2: Schematic structure of the electrical grid.
2.1.1 Distribution grid
Underground cables are favourable for distribution grids in urban areas, while overhead lines are most common for rural areas. With this said, the connection closest to the consumers are often underground even in rural areas [32]. The distribution grid can have various designs, depending on the application. The three major topologies are: double- cable, loop, and radial structure. In a radial grid the customers are fed after each other from one source. If a fault occurs in the radial, all the customers downstream from the fault are disconnected. The radial grid is mostly used in rural areas and is suitable for longer distances. A loop grid works like the radial grid, but the customers can be fed from two directions. Loop-grids are often used in urban areas. Double-cable structures are used for high demand city-areas, the reason for this is the high reliability of the system. The substations are fed with two cables and utilizes two transformers. The downstream grid, with the customers, are radial. The grid topologies can be seen in figure 3, where the arrows represents load connections and the x in 3b represents a breaker [2].
MV
LV
(a)
MV
LV
(b)
MV
LV
(c)
Figure 3: Distribution grid topologies, (a) double-cable, (b) loop, and (c) radial grid.
The DC-resistance of a conductor, at temperature T , is given by equation 2.1. ρT is the conductor resistivity at temperature T , l is the length of the conductor, and A represents the cross-section area.
RDC = ρTl
A (2.1)
The current in conductors, transmitting AC power, has a nonuniform distribution. The current density is higher near the surface, meaning that the conductor has a lower current density in the centre. This is called the skin effect and it intensifies with increased frequency. This phenomenon causes the AC resistance to be higher than the DC resistance, but at power system frequencies (50 or 60 Hz) the difference is merely a couple of percent.
The AC resistance is given by equation 2.2, I is the RMS current and Ploss is the active power loss. [7]
RAC = Ploss
|I|2 (2.2)
The lines in the distribution grid are often shorter than 80 km, thus the short line model can be used as representation. In the equivalent circuit (seen in figure 4) U1 represents the sending side voltage and U2 the receiving end voltage. The series impedance of the transmission line is defined by Z = R + jX.
R jX
I
−
+ U1
−
+ U2
Figure 4: Equivalent circuit of a short transmission line.
Based on Kirchoff’s second law, the voltage difference between the two nodes can be described by
U1 = U2+ (R + jX)I (2.3)
Assuming that the phase shift δ between the voltages is negligible, the voltage difference can be rewritten as
U1− U2 = R |I| cos(ϕ) + X |I| sin(ϕ) (2.4) , where the current drawn by node 2 can be defined as
I = (S2
U2)∗ ≈ P2− jQ2
U2 (2.5)
This results in equation 2.6, which quantifies the voltage drop for a short transmission line [16].
∆U2 = U1− U2 = RP1 + XQ1
U1 (2.6)
2.2 Power flow
To determine the power flow in a three-phase power system the power flow problem can be solved. The definition of the power flow problem is to compute the voltage magnitude and phase angle in every bus in a system. Two conditions for the system is that it should be balanced and operating under steady state conditions. When the power flow problem is solved, the reactive and active power flow in every component of the system can be derived. In the power flow problem, each bus k of the system is defined with four variables:
voltage magnitude Vk, phase angle δ, net real power Pk and reactive power Qk supplied to the bus. Each bus should have two known variables, used as input data in the model, and two unknowns (which will be computed). There are three types of buses:
• Slack (or swing): there is only one slack bus in each system. The slack bus is numbered as bus 1, and defined as U1 δ1 = 1.0 0° p.u.
• PQ (load) bus: Pk and Qk are used as input data.
• PV (voltage controlled) bus: Pk and Uk are used as input data. Generators and switched shunt capacitors are examples of voltage controlled buses.
The equivalent π-circuit is used to model the transmission lines. Corresponding series impedance Z and shunt admittance Y , together with power rating and bus configuration is needed as input. Transformers are modelled with their equivalent circuit. The input data for the transformer includes winding impedance Z, exciting branch admittance Y , bus configuration, and maximum power rating. The power system can be represented by the nodal equations defined by equation 2.7 [7].
I = YbusU (2.7)
U is the vector containing the voltage of each bus, and I is a vector containing the current going into each bus. For bus k equation 2.7 is given by
Ik =
N
X
n=1
YknUn (2.8)
2.3 Harmonics
Linear loads draws current which is proportional to the voltage, meaning that the current and the voltage is sinusoidal. Non-linear loads draw currents with waveforms that does not look like the waveform of the applied voltage. The non-linear currents are caused by a time-varying impedance, caused by electronic switches etc. [5]. The non-linear currents are non-sinusoidal and contains harmonic currents. Voltage distortions are formed when the harmonic currents are interacting with the impedance of the power grid. The distorted waveforms can be separated into sinusoidal components with varying frequency. The fundamental component has the same frequency as the grid (50 Hz in Sweden), and the harmonic components are integer multiples of the fundamental frequency, i.e. 100 Hz, 150 Hz, 200 Hz and so on. A general non-sinusoidal waveform repeating with angular frequency ω can be defined by equation 2.9a [29].
f (t) = 1 2a0+
∞
X
h=1
ahcos(hωt) + bhsin(hωt) (2.9a) With
ah = 1 π
Z 2π 0
f (t)cos(hωt)d(ωt) h = 1, 2, ..., ∞ (2.9b)
bh = 1 π
Z 2π 0
f (t)sin(hωt)d(ωt) h = 1, 2, ..., ∞ (2.9c) In figure 5, it can be seen how the third harmonic, with relative low magnitude, distorts the fundamental waveform.
Figure 5: Waveform as a result of the fundamental harmonic acting together with the third harmonic.
Devices operating with semiconductors are non-linear loads, and one of the most common sources of harmonics are static power converters. These kind of equipment generate characteristic harmonics, in steady state, which is determined by the number of pulses per cycle of the equipment. The characteristic harmonics, also known as dominant harmonics,
can be described by equation 2.10. h is the harmonic order, n is an integer, and p represents the number of pulses per cycle of the equipment [29].
h = np ± 1 (2.10)
The generation of characteristic harmonics is true if the AC power of the grid is completely sinusoidal and symmetrical. If there is any deviation from this ideal case, which is often the case for real applications, harmonics of non-characteristic order will occur. During balanced loading conditions for a four-wire system, the phase currents cancel each other out in the neutral wire (because of the 120° phase shift). If harmonics are present in the system ”triplen” harmonics (harmonics of order 3, 9, 15, ...) add up in the neutral wire and can cause a significant current [29]. The current in the neutral can be determined by equation 2.11 [5].
Ineutral = q
I12 + I32+ I52+ I72+ I92+ I112 + ... + In2 (2.11) Total harmonic distortion (THD) is an index for power quality, which is used to evaluate power systems with harmonic presence. The total harmonic distortion for both voltage and current can be determined by equation 2.12 and 2.13 respectively, where U1 and I1 is the fundamental component [5].
T HDU =
pP∞ h=2Uh2
U1 (2.12)
T HDI =
pP∞ h=2Ih2
I1 (2.13)
Load loss for a transformer can be categorized into I2R loss and stray loss. The later are due to stray electromagnetic flux in core, core clamps, windings etc. Stray losses are divided into stray loss in other components than the windings (POSL) and winding stray loss (PEC). The winding stray loss includes eddy current loss in the winding conductor and losses caused by circulating current between strands. Equation 2.14 can be used to define the load losses.
PLL = I2R + PEC+ POSL (2.14)
Due to the harmonic components in the load current, the I2R loss are increased with harmonic content. The winding eddy current losses are proportional to the square of the current and the square of the frequency, according to equation 2.15. High winding temperature rise can be caused by excessive winding eddy current losses. Other stray loss are also increased by harmonic content, but temperature rise in the corresponding components are not as severe as in the winding. The DC component of the harmonics will cause an increased magnetizing current and thus increase the sound level [17].
PEC = PECR
hmax
X
h=1
Ih2h2 (2.15)
PEC represents the eddy current losses due to non-sinusoidal content, and PECR describes the winding eddy current losses at rated loading. Ih is the RMS-current (per unit) at harmonic number h.
2.4 Power quality
Power quality is a term used for a wide range of disturbances in the power system.
The definition of power quality varies, depending on the perspective. From a utility company point of view, power quality could be defined as reliability of the system. For a manufacturer of power equipment, the properties of the power source that will make the equipment work correct could be their definition of power quality. The consumer perspective is probably the most influential for power quality issues. Electrical Power System Quality uses the following statement as a definition of power quality: “Any power problem manifested in voltage, current, or frequency deviation that results in failure or misoperation of customer equipment”. Even though power quality is the most common used term, it is in fact voltage quality that is taken under consideration for power quality issues [6].
2.4.1 Grid codes
The Swedish Energy Market Inspectorate has guidelines for what could be viewed as good power quality. The following sections identifies what is needed for good voltage quality.
For systems with nominal voltage up to 1000 V, the phase voltage is used to quantify the voltage quality indexes. The following sections are taken from the guidelines in [11]. A 10-minute value (Ush) of the voltage is defined as the RMS of the 3-second values (Uvs) of the voltage during a 10-minute period, according to equation 2.16. Where N is the number of 3-second values in the 10-minute period. And tk represents the end of the 10-minute interval [3].
Ush(tk) = v u u t
1 N
k
X
i=k−N +1
Uvs2 (ti) (2.16)
2.4.1.1 Slow voltage variation
During the period of one week, the 10-minute value of the voltage should be confined between 90% and 110% of the nominal voltage.
2.4.1.2 Voltage unbalance
For symmetric voltage, the RMS-value and the phase difference of the three phases should be the same. During the period of one week the 10-minute value of the voltage unbalance should be less or equal to 2 % [11].
Voltage unbalance can be quantified by comparing the zero- or negative-sequence compo- nent to the positive-sequence component, the voltage unbalance will be given in percent.
Single phase loads are usually the source for voltage unbalance [19]. The sequence voltages are defined by equation 2.17. Where U0 is the zero-sequence, U1 is the positive sequence, and U2 is the negative sequence component. a is defined as 1 120° [7].
U0 U1 U2
= 1 3
1 1 1
1 a a2 1 a2 a
Ua Ub Uc
(2.17)
2.4.1.3 Short term voltage drop
For systems with a nominal voltage up to 45 kV, short term voltage drops that corresponds to area C in table 1 are not allowed. If a voltage drop occurs that corresponds to area B, the grid owner is responsible to take action to prevent the disturbance (if the preventing actions are feasible and comparable to the disturbance).
Table 1: Regulations for short term voltage drop for systems up to 45 kV.
U [%] Time period [ms]
10 ≤ t ≤ 200 200 < t ≤ 500 500 < t ≤ 1000 1000 < t ≤ 5000 5000 < t ≤ 60000 90 > u ≥ 80
80 > u ≥ 70 A
70 > u ≥ 40 B
40 > u ≥ 5 C
5 > u
2.4.1.4 Short term voltage rise
For nominal voltage up to 1000 V, short term voltage rises with properties that corre- sponds to area C in table 2 are not allowed. The grid owner is responsible to take action to prevent voltage rises in area B (if the preventing actions are feasible and comparable to the disturbance).
Table 2: Guidelines for short term voltage rise for systems up to 1000 V.
U [%] Time period [ms]
10 ≤ t ≤ 200 200 < t ≤ 5000 5000 < t ≤ 60000
u ≥ 135 C
135 > u ≥ 115
115 > u ≥ 111 B
111 > u ≥ 110 A
2.4.1.5 Rapid voltage change
A rapid voltage change (RVC) is defined as a fluctuation where the RMS-value of the voltage changes faster than 0.5 % per second, and the voltage is confined between 0.9 p.u.
and 1.1 p.u. before, during, and after the change. There is two types of rapid voltage change, stationary (∆Ustat) and maximum (∆Umax). A stationary RVC is defined by the difference between the RMS voltage before and after the change. The maximum RVC is defined by the maximum or minimum value during the fluctuation compared to the value before the event. The sum of the number of rapid voltage changes added with the number of short term voltage drops corresponding to area A in table 1 should not exceed the limitations shown in table 3.
Table 3: Maximum number of allowed rapid voltage changes during 24 hours.
RVC Unom ≤ 45 kV Unom > 45 kV
∆Ustat ≥ 3% 24 12
∆Umax ≥ 5% 24 12
2.4.1.6 Voltage harmonics
For grids with nominal voltage equal to or below 36 kV the voltage THD should be lower than 8 %. The allowed presence of individual harmonics can be seen in table 4.
Table 4: Allowed maximum values for individual harmonics for systems up to 36 kV.
Odd Harmonics
Even harmonics Non multiple of 3 Multiple of 3
Harmonic Relative
magnitude [%] Harmonic Relative
magnitude [%] Harmonic Relative magnitude [%]
5 6.0 3 5.0 2 2.0
7 5.0 9 1.5 4 1.0
11 3.5 15 0.5 6 0.5
13 3.0 21 0.5 8 0.5
17 2.0 - - 6 - 24 0.5
19 1.5 - - - -
23 1.5 - - - -
25 1.5 - - - -
2.4.2 Guidelines by Energif¨oretagen
The Swedish trade organization Energif¨oretagen have developed guidelines for connec- tion of PV-systems. General protection guidelines for production units in low-voltage distribution grids can be seen in table 5.
Table 5: Protective relay specifications for production units connected to the low-voltage grid [10].
Category Time [s] Limit
Over-voltage (step 2) 60 230 V +11 % Over-voltage (step 1) 0.2 230 V +15 %
Under-voltage 0.2 230 V -15 %
Over-frequency 0.5 51 Hz
Under-frequency 0.5 47 Hz
Loss of mains 0.15 -
The recommended voltage deviation for connection of the maximum power of the pro- duction source should not exceed the values in table 6.
Table 6: Guidelines for voltage deviation for PV-systems connected to the grid.
Maximum voltage deviation
At the customer connection 5 % At the point of common coupling 3 %
For a three-phase connection, the short circuit power at the customer connection point should be more than 20 times larger than the installed power. The short circuit power of
the grid should be at least 34 times larger than the installed power at the point of common coupling [10]. Equation 2.18 is recommended by Svensk Energi to quantify the voltage drop for connection of a production unit. P and Q represents the maximum produced active and reactive power. R and X represents the impedance of the grid, and U1 is the reference voltage. For three-phase production, three-phase short circuit impedance is used for R and X, and the phase to phase voltage is used as the reference voltage [10].
∆U
U1 = RP + XQ
U12 · 100% (2.18)
Two extreme cases are used to evaluate slow voltage fluctuations, (i) maximal loading and no production, and (ii) minimal loading and full production. The limitations can be seen table 7 [10].
Table 7: Guidelines for slow voltage deviation by Energif¨oretagen.
Recommended short term voltage deviation Total voltage deviation MV+LV ± 8 %
Only LV ± 5 %
2.5 Balancing techniques
2.5.1 Magtech Voltage Booster
The Magtech Voltage Booster (MVB) is able to lift and stabilize voltages to correct unbalanced phase voltages for low-voltage lines. Unbalanced situations are often caused by large single-phase loads. The MVB consists of a Magtech adjustable inductor (MCI) connected to an autotransformer. The MCI is made out of a main copper winding around an iron core, the winding is supplied with an AC-current which produces an AC-flux inside the core. A secondary copper winding is connected to the core, which generates a DC-flux orthogonal to the flux of the main winding. By adjusting the DC-current of the secondary winding, the equivalent inductance of the primary winding is changed. Using this setup, the voltage over the auto transformer can be controlled with the DC-current in the secondary winding of the MCI. In figure 6a the red wire represents the DC-winding, and the blue wire represents the AC-winding. In figure 6b the single phase circuit of the MVB can be seen, this booster setup is used for all three phases. Regulator modules are used to measure the phase-to-neutral voltage for each phase, the regulators control the variable inductors individual to boost the voltage [21].
(a) (b)
Figure 6: (a) magtech adjustable inductor [34], (b) single phase equivalent of the MVB [21].
2.5.2 Energyhub
Ferroamp is promoting a DC-microgrid for residential and office-buildings. PV-systems, batteries, and EV-chargers can be implemented in their system. The main component in the DC-microgrid is the EnergyHub, which in principle is a bi-directional inverter with control and measurement systems. The EnergyHub is controlling the power flow to and from the property. Reduced power loss, due to fewer power conversions, is used as a promoting argument [14]. The EnergyHub includes the adaptive current equalization (ACE) function which is able to balance the currents in the input three phase power. In case of an unbalanced load, the technology utilizes the low-loaded phases to compensate for the current needed by the high-load phase/phases. This means that the current is equal (in magnitude) in all three phases at the input to the property, then the EnergyHub takes action and correct the currents according to the loading situation. The ACE-technology allows the main fuse to be smaller, and thus saving money and work [15]. In figure 7, an example of the adaptive current equalization can be seen.
Figure 7: Adaptive current equalization balancing the currents to an unbalanced load [15].
2.6 Photovoltaics
By the end of 2017, the total installed global PV capacity was noted at 400 GW. The PV capacity grew with 4300 % in the ten year period between 2007 and 2017 [18]. The global price of photovoltaic modules has been decreasing significantly the last 30 years. On average the price per Wphas been decreased with 10 % each year [23]. By the end of 2017, the total installed power of grid connected PV-systems in Sweden was 230.99∗ MWp. The majority of the installations are below 20 kWp. The system price for a residential roof- mounted grid connected PV-system in Sweden has been decreasing drastically. A price of 63.3 SEK/Wp was noted in 2010, and 14.8 SEK/Wp in 2017 (excluding VAT). The hardware of the system constitutes the major cost of the system. For a grid-connected roof-mounted residential system of 5 kWp, the cost can be divided into the following categories. Modules and inverter stands for 41 % and 20 % of the total cost, respectively.
The relative cost for installation work is 18 %, while permits and commissioning stands for 8 % of the total cost. It should be mentioned that the cost of the system (SEK/Wp) is decreased when the installed capacity is larger [20].
2.6.1 Solar cell
The absorber material of the solar cell consists of a semiconductive material forming a pn- junction. Photons from the sunlight are absorbed by the semiconductive material, if the energy of the photon is higher than the bandgap of the material an electron and hole pair is generated. The free electron and hole travels to different sides of the pn-junction, which is connected to an external circuit. Thus, the photocurrent of the solar cell is generated and power can be extracted [23]. The equivalent circuit of a solar cell can be seen in figure 8a, including series resistance Rs and shunt resistance Rsh [22]. IV-characteristics of a solar cell describes its properties, IV-characteristics of a generic solar cell can be seen figure 8b. The maximum power point (MPP) is defined as the point with the largest magnitude of the product of voltage and current. The maximum power from the cell is
∗According to grid owners, collected by SCB. Sales statistics shows higher installed power, 307.4 MWp. The difference may depend on uncertainties in sales statistics or errors by grid owners.
defined as Pmpp= VmppImpp. The efficiency of the solar cell is defined as output power at MPP compared to the incoming optical power Popt.
η = Pmpp
Popt = F F VocIsc
Popt (2.19)
Iph
Rsh Rs
−
+ U
(a)
(b)
Figure 8: (a) circuit equivalent of a solar cell, (b) IV-characteristics for a generic solar cell.
2.6.2 PV-system
Several solar cells are connected in series and parallel together in a module. The proper- ties of the module is determined by the configuration of the solar cells. The photovoltaic modules are series connected in strings, the strings are connected in parallel. The voltage of one string is the sum of the individual voltage of the modules. The current adds up as the sum of the current of the individual strings [23].
The principle structure of a grid-connected PV-system consists of PV-modules, DC-DC converter, inverter, and filter. A DC-DC converter is used to convert an input a voltage to a desired voltage level. The converter is vital for maximum power point tracking (MPPT) for the modules. For grid connections, a step-up DC-DC converter is often used to boost the voltage from the PV system. An inverter is used to convert the generated DC power from the PV-system to AC power compatible for consumption. Inverters can be catego- rized in converting method (transformer based or high frequency switching), and type of connection (utility connected or stand-alone). For grid-connected systems, inverters using high frequency switching with PWM (pulse width modulation) are favourable to generate power with sufficient quality. Four main topologies are used for grid connected inverters:
central inverter, string inverter, multi-string inverter, and module inverter. The filter is used between the inverter and the grid to reduce high order harmonics (generated by the PWM), and consists of an inductor and a capacitor [22].
2.7 Electric vehicles
Vehicles able to run on electricity can be divided into three groups: Battery electric ve- hicle (BEV), Plug-in hybrid electric vehicle (PHEV), and Hybrid electric vehicle (HEV).
BEVs, also known as just EV, use rechargeable batteries to drive. A PHEV has both a rechargeable battery and a traditional fuel tank, the battery can be charged by connect- ing an external source or by regenerative breaking. HEVs utilize regenerative breaking to charge their battery. They are able to use the battery to travel a short distance with low speed, compared to PHEVs which can travel longer distances with normal speed [13]. At the end of 2018, the number of BEVs and PHEVs was noted at 68804 in Sweden. 72 % of the chargeable vehicles are PHEV, and the rest is BEVs (light trucks and motorbikes are included in the statistics). Some of the most popular BEVs are: Nissan Leaf, Tesla Model S, and Renault Zoe. For PHEV, the most popular models are: VW Passat GTE, Mitsubishi Outlander, and KIA Optima. Power Circle, a Swedish trade organization for electrical power, are predicting 2 500 000 chargeable vehicles in Sweden in 2030. Accord- ing to the prediction, 68 % of the chargeable vehicles is going to be of type BEV [27].
The charging modes of the vehicles can be divided into four categories: Normal, semi-fast, fast, and temporary. Normal charging is defined as powers equal to and below 3.7 kW. The charging station is recommended to be “mode 3 type 2”, the charging is performed with the type 2 cable utilizing one phase (230 V, 16 A). The technology for semi-fast charging is not specific, but some possible methods are 3-phase and DC. Semi-fast charging (3.7 – 50 kW) can become relevant in the future, when more charging techniques are specified. Fast charging is defined as above and equal to 50 kW. It utilizes DC power with an external charging station (which includes a rectifier). Two common types of techniques used for fast charging are Chademo and CCS (Combined Charging System) [31]. Another type of fast charging is the Tesla Supercharger [27]. Temporary charging can be used when there is no charging station around. Temporary charging uses a single-phase domestic earthed socket (230 V, 10 A or less), which results in a charging power up to 2.3 kW [31].
Public charging stations can be divided into normal-power recharging point (≤ 22 kW) and high-power recharging point (> 22 kW) [12].
3 Method and data
3.1 Customer
The customer, located in the rural parts of Norrt¨alje municipality, is distanced with 775 m of transmission lines from the feeding substation. The property is a small-scale farm, connected with a 25 A main-fuse. An 80 m cable is used to connect the residential connection to two other buildings where the PV-system is connected, and where the charging station is located. The cable used for this application is of type type EKKJ6.
The electric vehicle is a Nissan Leaf (2016), and it is charging with a single phase charger at 25 A (5.75 kVA). According to the owner, no specific pattern is in use for charging the vehicle. The imported electricity to the property (subtracting the PV-production from the load profile) for 2018 can be seen in figure 9.
Figure 9: Imported electricity profile for 2018.
The PV-system is located on the roof of two buildings, one roof with 39 modules and the other with 24 modules. Individual maximum power point trackers are used for the modules. The larger building is from now on referred to as building 1, and the other one referred to as building 2. The total installed power 16.38 kWp, which corresponds to 104.5 m2, is connected to a central three-phase inverter. See table 8 for properties of the PV-system.
Table 8: Properties of the PV-system.
Module ECSolar 260W
Inverter SolarEdge SE17k
Installed power 16.38 kWp Tilt (building 1) 34.9° Tilt (building 2) 32.5° Azimuth*(building 1) 232° Azimuth (building 2) 225°
* Azimuth is defined as the angle in the horizontal plane, where north is equiva- lent to 0° and south is defined as 180°.
3.2 Power quality measurements
To evaluate the power quality at the location of the customer, three power quality mea- surements were analysed. The first one was done at the time of the reported distur- bance, 2018-03-09 – 2018-03-19, by Norrt¨alje Energi. A second measurement were done by Norrt¨alje Energi after the MVB was installed, 2018-05-31 – 2018-07-16. Both of the two first measurements were set up at the connection point of the customer (cable cabi- net). A third measurement were done as an initiative of this thesis, it was set up at the location of the inverter (of the PV-system) in the period of 2019-02-27 – 2019-03-12. The measurement was set up at the inverter, which is the point of the reported disturbance, to further investigate the cause of the disconnection. The power quality measurement was done using a Metrum SPQ. Metrum SPQ measures according to IEC 6100-4-30, class A [24]. The software Metrum PQ Viewer was used to evaluate the power quality. With Metrum PQ Viewer it is possible to view 10-minute values of the following entities as time series:
• Power
• Flicker
• Harmonics (individual and THD)
• Voltage unbalance (sequence components and the relative difference between the negative sequence and the positive sequence)
• Voltage and current (average, min, and max values)
• Frequency
• Energy
The 10-minute values are based on half-period RMS values, which are measured with a sampling frequency of 12.8 kHz of the waveform. This means that a value is measured each 0.01 second (12(50 Hz1 )), and thus the 10-minute value is the average of 60 000 values. It should be noted that the maximum and minimum value is defined as the maximum/min- imum value during the 10 minute measurement period. The software also features an event log with high time resolution of transients, sags, and swells. Metrum PQ viewer has the option to evaluate the results with different power quality norms, for this application
the norm EIFS 2013 under 1 kV was used. Weekly reports can be concluded by the pro- gram, the reports summarise the data and gives results for each power quality category (according to the chosen standard).
3.3 Trimble NIS
Trimble NIS is a software for network information that can be applied to electrical grids, water and sewer systems, district heating, and communication systems. Norrt¨alje Energi uses Trimble NIS for their electrical grid. The grid model is based on objects stored in a database. The residential loads in the grid are defined by a consumption category, and the load profile for each load is determined by a typical curve (based on betty-kurvor 1.2).
A simulation were performed with a solution regarding power distribution - dimensioning (sv. Effektf¨ordelning - dimensionering) and short circuit. The following options were used:
• Temperature: Mean-year
• Statistical probability: 90 %
• Calculated hours: Whole day
• Calculation voltage: From feeding transformer
• Degree-days: 3701
The maximum current and minimum voltage at each bus was used for validating the OpenDSS-model. A simplified single-line diagram can be seen in figure 10. Where bus 309616 represents the residential connection of the customer. Bus 670037, which is men- tioned in the result, is located between 670035 and the residential load 310024.
MV
670001 T670 Loads
KS6701
Loads Loads
670035
310024 (load)
309616 Phouse
PV
EV
PV-system Figure 10: Simplified single line diagram of the distribution grid.
3.4 OpenDSS
Open Distribution System Simulator (OpenDSS) is a software for electric utility distri- bution systems. The fundamental function of the program is RMS steady-state analysis, which is often used for utility distribution systems. But it also features other modes, which can be used depending on the aim of the simulation. Some solution modes are:
• Snapshot power flow
• Daily power flow
• Yearly power flow
• Fault study
• Harmonics
OpenDSS is used in this project due to the fact that it handles single-phase behaviour and harmonic analysis. To achieve a representative model of the grid, parameters for the objects was taken from the database in Trimble NIS. The overlying 11 kV grid was modelled as a voltage source with parameters seen in table 9. OpenDSS utilizes the single-phase short circuit to characterize the single-phase behaviour of the system. The model in Trimble NIS is completely balanced, and thus only defined by the three-phase short circuit current. This led to the assumption that the single-phase short circuit, in the OpenDSS-model, is the same as the three-phase short circuit current (achieved from Trimble NIS). The feeding transformer was modelled with values according to table 9, where the data is retrieved from Trimble NIS.
Table 9: Properties for the electrical grid.
Overlying grid Voltage 11 kV
3-phase short circuit current 1189 A
Transformer
Power 315 kVA
Voltage 11/0.4 kV
Connection Delta-Wye
Short circuit reactance 3.6 % Short circuit resistance 1.14 %
No-load resistance 0.15 %
A system with four phases (3 phases and a neutral) was used to model the transmission lines. Due to the fact that the impedance differ between the active conductors and the neutral conductor for some lines, the phase conductors and the neutral conductor was modeled separately. This implies that two separate elements was used between each bus, one for the neutral wire and one for the phase conductors. Positive- and zero-sequence values for resistance, reactance, and susceptance was used in the model. The values can be seen in table 10. Positive- and negative-sequence properties of the transmission lines are assumed to be the same by default in OpenDSS. The resistance in table 10 is defined at 20
°C. The impedance for the neutral wire is used as positive-sequence values in the model.
Positive- and zero-sequence components were assumed to be the same in the model, due to lack of zero-sequence data.
Table 10: Transmission line parameters.
Line Type R1 [Ω/km] X1 [Ω/km] Rn [Ω/km] Xn [Ω/km] B1 [µS/km]
ALUS50 Aerial cable 0.641 0.085 0.641 0.085 65.973
ALUS95 Aerial cable 0.32 0.08 0.32 0.08 78.54
EKKJ4 Cable 4.61 0.099 4.61 0.013 84.823
EKKJ6 Cable 3.08 0.093 3.08 0.017 91.106
EKKJ10 Cable 1.83 0.087 1.83 0.016 100.351
FKKJ16 Cable 1.15 0.082 1.15 0.018 113.097
N1XV50 Cable 0.641 0.081 0.641 0.081 65.973
N1XV240 Cable 0.125 0.078 0.125 0.078 87.965
The residential loads in the system was modelled as three-phase default loads, defined by three-phase active power and power factor. Nominal phase-to-phase voltage (400 V) was used as an input. The loads are defined by the default model 1, i.e. constant active and reactive power. In power flow mode, the default three-phase load is defined as balanced and wye connected. The residential loads in the distribution system can be seen in ap- pendix A. The maximum power for each load was achieved from calculations in Trimble NIS. The minimum load is assumed to be 10 % of the maximum load for homes used for permanent living. Summer cottages are assumed to have a minimum load of 0 kW. The grounding of the system was modelled as the neutral directly earthed at several places in the system, according to Trimble NIS. A 2 Ω-resistance was used as resistance between node 4 (neutral wire) and node 0 (perfect ground).
The electric vehicle was modelled as a single-phase load at the same bus as the PV-system.
The load was connected between node 1 (phase A) and node 4 (neutral). The charging complex power of the vehicle was assumed to be 5.75 kVA (25 A · 230 V), with a power factor of 0.98 lagging [26]. To evaluate different loading situations, eight scenarios were simulated (which can be seen in table 11).
Table 11: Simulation scenarios for the OpenDSS- model.
Scenario Load PV-production EV-charging
1 Max Max On
2 Max Max Off
3 Max Min (0 %) On
4 Max Min (0 %) Off
5 Min Max On
6* Min Max Off
7 Min Min (0 %) On
8 Min Min (0 %) Off
* Simulated with 420 V as the input data at the secondary side of the transformer, due to con- vergence failure.
3.4.1 Harmonic analysis
Objects in OpenDSS can be assigned a harmonic spectrum. The spectrum defines the harmonic currents that are injected into the system. A spectrum is usually defined by:
number of harmonics, harmonic order, percentage magnitude of the harmonic currents (relative to the fundamental current), and phase-angle. Before solving the harmonic power flow, a snapshot power flow of the system must be computed and reach conver- gence. In harmonic mode, OpenDSS solves the system for every frequency defined in the spectrum/spectrums of the system. To analyse the result of the harmonic sources, monitors are placed at strategic positions in the grid. In harmonic mode, objects that are assigned a spectrum are modelled as a Norton equivalent, which can be seen in figure 11. Loads in OpenDSS are defined as a Norton equivalent with the impedance divided between parallel RL and series RL with the ratio of 50/50 as default.
jB(ω) G
jX(ω)
R If und· Spectrum(ω)
Figure 11: Norton equivalent for the harmonic source in OpenDSS.
To evaluate the harmonic impact in the system, four scenarios were simulated. The sce- narios can be seen in table 14. PV-inverters tend to have higher harmonic emissions when operating at lower power output, thus 25 % production is investigated. The generator, modelling the PV-system, is operating at 25 % of its peak power when it is assigned the spectrum corresponding to 25 % production. A phase-angle of 0° was used for every harmonic for the PV-inverter, due to lack of data. Components in OpenDSS are assigned a harmonic spectrum by default, which was removed during the harmonic analysis to be able to quantify the harmonic impact of the PV-system and EV-charger.
Table 12: Harmonic spectrum for the PV-system at different power outputs [4].
Harmonic (n) Output power: 25 % Output power: 100 % Relative magnitude [%] Relative magnitude [%]
1 100 100
3 3.5 1.8
5 5 1.2
7 3 0.3
9 1 0.3
11 0.7 0.2
Table 13: Current harmonic content for Nissan Leaf [1].
Harmonic (n) Relative magnitude [%] Angle [°]
1 100.00 -26.00
3 25.00 -94.00
5 17.00 -96.00
7 14.20 -72.00
9 9.69 -68.00
11 5.04 -49.00
13 1.80 -49.00
15 0.37 -46.00
Table 14: Simulation scenarios for the harmonic analysis in OpenDSS.
Scenario Load PV-production EV-charging
1 Max 100% On
2 Max 25% On
3 Min 100% On
4 Min 25% On
The increased winding eddy-current losses is calculated with equation 2.15, where Ih (p.u.) = Ih (A)
IR (A) (3.1)
The fundamental current is used as the rated current IR. The result is given as relative increase of the winding eddy-current losses.
3.4.2 Validation
To validate the model, a simulation was performed without the PV-system and the electric vehicle charger. The resulting voltage and current for each bus in the system was compared to values from Trimble NIS, which represents the lowest calculated voltage at each bus and the highest recorded current injected into each bus. The voltage at the secondary side of the transformer was adjusted in the model, to match the value from Trimble NIS.
421.7 V was used as the reference voltage for the secondary side of the transformer in the validated model. Data for the validation can be seen in appendix B.
3.5 Alternative solutions
3.5.1 Grid reinforcement
An alternative solution to the problem is reinforcements of the distribution grid. The following two changes in the grid is taken under considerations together:
• Change the ALUS50, between bus KS6701 and 670030, to an ALUS95
• Use double ALUS50 between bus 670030 and 670005
Properties for the lines can be seen in table 10. To evaluate the situation, the new lines in the grid is implemented in the OpenDSS model. Simulations for the worst case scenario for both voltage drop, voltage unbalance, and harmonics are performed.
3.5.2 Energyhub
To evaluate the adaptive current equalizer by ferroamp, the OpenDSS model is simulated with maximum load and no PV-production. The EV-charging is modelled as a three- phase load connected at the residential connection (309616). In this way it is possible to determine the phase-voltage for the balanced loading situation that the ACE would create. The phase voltages at the house is used to determine the voltage drop caused by the EV. Using the short line transmission line model, seen in equation 3.2, the voltage at the PV-bus can be determined. Us is the sending side voltage, taken from the OpenDSS- simulation. IR is the receiving side current and is equal to the single phase charging current 25 11.5° A, as stated in section 3.4. Z is the series impedance of the line, and is determined by the length of the cable and the transmission line parameters in table 10 for EKKJ6.
US IS
=1 Z 0 1
UR IR
⇒ UR= US − ZIR (3.2)
The voltage at the PV-bus is assumed to be the same as the sending side (309616) for phase B and C. The voltage at the receiving end UR is used for phase A. Equation 2.17 is used to determine the voltage unbalance at the PV-bus.
