The Effect of Harmonics on the Electrical Grid due to Electric Vehicle Chargers _____________________________

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The Effect of Harmonics on the

Electrical Grid due to Electric Vehicle Chargers

_____________________________

Ingemar Solander Araúz

ISRN UTH-INGUTB-EX-E-2020/009-SE

Bachelor Thesis 15hp

December 2020

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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

The Effect of Harmonics on the Electrical Grid due to Electric Vehicle Chargers

Ingemar Solander Araúz

In this thesis the effect of harmonics on the electrical grid from electric car chargers, specifically the effect on distribution

transformers, is analyzed. The study was performed on the electrical grid of two areas provided by the electrical company Dala Energi. Electric car chargers are added to each customer connected to the electrical grid in both areas to examine the effects of harmonics on the distribution transformers. A model of the electrical grid of each area was recreated and simulated with the open source program OpenDSS. The effects of the added harmonic load on the electrical grid was evaluated in a range from 10% to a 100% of the consumers connected to the grid.

The results of this study show an increase in losses due to harmonic distortion. However, the losses are less significant when the added electric car charger load is distributed between all three phases of the grid compared to one phase. All the added harmonics, except the 9th harmonic, maintain acceptable levels set by The Swedish Energy Market Inspectorate. The impact of the 9th harmonic can be reduced by installing filters. The main conclusion of this thesis is that to reduce the effects of harmonic on the grid the harmonic load should be distributed on all three phases. Also scheduling the charging time of the cars can be implemented to further even out the load variations on the electrical grid.

Tryckt av: Uppsala Universitet

ISRN UTH-INGUTB-EX-E-2020/009-SE Examinator: Johan Abrahamsson Ämnesgranskare: Karin Thomas Handledare: Juan de Santiago

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Popular science summary

Electric cars have become more common in society and thus the amount of electric car chargers have increased as well. Many new electric car chargers have been placed close by major roads, example in parking lots of restaurants, by conventional gas stations etc. However, the most common place where the electric car is charged is at home and the most common time to charge is when everyone returns from work in the afternoon/night. This causes new problems to the electric grid due to the addition of harmonic distortions when charging the electric car.

Harmonic distortion could result in power losses if not taken under consideration. Therefore, the Swedish Energy Market Inspectorate established regulations to control and reduce the effect of harmonics on the Swedish electrical grid.

The effect of harmonic loads on the electrical grid is analyzed for two areas, A and B. The grid model for both the areas are provided by Dala Energi. The grid models include data for all cables, transformers and connection points. The aim of this project is to evaluate how well the electrical grid of the areas can handle the added harmonic load. The harmonic distortion in transformers of the areas are examined. Secondly, the loss due to harmonic currents in the transformer are analyzed as well.

The provided data for the electrical grids are used to model the studied areas with the open source program OpenDSS. A harmonic load, corresponding to a 1-phase electric car charger, is gradually connected to the customers in the area, from 10% to a 100% load. This is analyzed for two connection configuration, first phase versus a mixed dispersion on the 3 phases. The results are later compared to investigate the limitations on the electrical grid with the added harmonic load.

The results of the simulations in OpenDSS show a similar outcome for both areas. The individual voltage harmonic distortion is reduced by distributing the load over all three phases compared to the case when all the chargers are connected to the same phase. The load loss due to

harmonic currents, both eddy currents and stray losses, are reduced when the harmonic load is spread out over all three phases. The max value for the loss factor K is topped later with a higher load on the area when all three phases are utilized. The addition of the harmonic load will increase the eddy current losses about 3.5 and the stray losses 1.3 times when 100% the households in the areas are loaded. Much due to the increased heat losses from the added harmonic currents in the transformer.

The conclusion of this project is the importance of an evenly distributed load to reduce the effects of harmonics in the electrical grid. The limits set to control the effect of harmonics on the electrical grid may have to be reevaluated in order to cope with increased use of electric cars. Other options that could be implemented to reduce harmonics arising from charging of electric cars are active or passive filters to manage the maximum limits set for each harmonic.

Additionally, a charging schedule depending on the main power consumption of the household could contribute to a reduction in loss. By changing the power consumption used to charge the

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ii car, reduce or increase the current depending on the main power consumption of the house, the total load on the electrical grid would stay more consistent.

Exekutiv sammanfattning

Examensarbetet undersöker inverkan av övertoner från elbilsladdare på det elektriska nätet, specifikt på transformatorerna. Ett samarbete via Uppsala universitet samt elbolaget Dala energi möjliggör detta projekt. Kartor över elnätet för två områden lånas ut från Dala energi för att användas som underlag i detta projektarbete. Data för elnätet i de två områdena används för att bygga upp en liknande miljö i simuleringsprogrammet OpenDSS. I områdena är alla hushåll preciserade i uppkopplingen till elnätet, samma uppkopplingspunkt används för att koppla på enfaselbilsladdaren i from av en övertonslast. Sedan görs ett antal tester för att undersöka kapaciteten hos de två områdena när olika stora övertonslaster kopplas på, 10% till 100% av hushållen. Belastningen jämförs mellan två olika uppkopplingsalternativ för

enfasladdaren, alla uppkopplade till första fasen mot en utspridd uppkoppling på alla tre faser.

Resultaten visar att de individuella spänningsövertonerna i transformatorerna minskar i storlek när de uppkopplade laddarna sprids ut på alla tre faser i nätet. Transformatorförluster, som uppstår p.g.a. övertoner i strömmar, minskar när andelen hushåll med elbilsladdning dvs övertonslasten ökar.

Då elbilsladdarna endast kopplas mot en fas överskrids Energimarknadsinspektionens

gränsvärden för övertoner i spänningen vid en lägre andel inkopplade laddare än för fallet där laddarna fördelas jämt mellan de tre olika faserna.

Acknowledgements

This thesis is the final project to conclude my bachelor’s degree in electrical engineering at Uppsala University. The thesis was a collaboration between Uppsala University and Dala Energi, which provided the electrical grid. The study was conducted during spring of 2020 and covers 15 credits.

I would like to thank and show my gratitude to Dala Energi which enabled this thesis by sharing information on their electrical grid. Specifically, I would like to thank Fredrik Nyman at Dala Energi for all the data he provided me with. Also, I would like to thank Juan de Santiago at the Electricity Division of Uppsala University for his help and guidance throughout this thesis. Lastly, I want to show my appreciation to Karin Thomas and Johan Abrahamson at the Electricity Division of Uppsala University for their feedback to finalize this thesis report.

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1 Introduction

In recent years, the availability of electric cars have increased. The charging infrastructure to enable the use of the electric cars impose a new type of load connected to the electrical grid.

Due to the load when charging the electric cars the electrical grid will be exposed to an increased harmonic level. These harmonics could contribute to higher losses and reduced efficiency on the grid.

Many previous studies on the effect of harmonics on the electrical grid have been conducted [1]. This study continues a previous study made on the charger for a Nissan Leaf electric car [1].

The same measured harmonic content of the Nissan electric car charger made in that study was used as the load content for chargers in simulations preformed in this analysis. Another similar case study made on a low-voltage distribution grid here in Sweden was used to determine key loss calculations to evaluate the effect of harmonics on the electrical grid [2].

The electrical grid will be affected in different ways by the harmonic distortion containing both non-linear currents and voltages. The consequence is mainly heat losses in the cables of the electrical grid due to the harmonic irregularities when power is consumed by the electric cars charging their batteries.

The harmonic distortion could be reduced with different filters or by charging at lower current- rates during the night. Limits are set to assure a somewhat equivalent “electric quality” to consumers. These limits are defined to restrict the effects of harmonic distortion on the electrical grid.

In this project the effect of harmonics on the transformer in two areas are analyzed. The simulations show the amount of car chargers each area can handle before exceeding the limits set for harmonic distortion. The electric car chargers are modelled as external loads and are added to every customer connected to the electrical grid in the area. The amount of chargers are increased from 10% to 100% of the customers in each area.

1.1 Problem description

The addition of electric car chargers on the electrical grid results in new losses due to the harmonic distortion. It will affect various parts of the grid differently. There are rules and regulations, to limit the effect of harmonic distortion on the electrical grid, set by The Swedish Energy Market Inspectorate [3].

1.2 Aim of the thesis

The aim of this thesis is to investigate the capacity on electrical grid of two areas when adding the electric car charger loads. The individual voltage harmonic distortion level will be examined, the amount of load the grid can handle before exceeding the approved level. Furthermore, the losses due to harmonic distortion in the currents of the transformer will be analyzed. Besides the amount of harmonic load in the areas, the effect of the 1-phase charger with different configurations will be studied.

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2 Theory

2.1 QGIS to open Shape files

The maps over the transmission/distribution line layout, obtained from an energy company, was of the form factor shapefile. This type of file is made up of different layers, consisting of points, lines and other figures, that if put together creates the layout of a map. In order to utilize the data of these shapefile the program QGIS was used.

QGIS is a graphical program which is used to build and map out different areas [4]. By adding layers on top of each other, the topology of a region can be created. In this case it is used to show all the transmission lines, distribution lines and connecting points of an area. Each of these points on the map have their own id, together with an attribute list and coordinates for the specific point on the map. The attribute list consists of impedance values, lengths, coil info, and phase configuration, all depending on the object type (line, transformer, load etc.) The

information was exported to an excel list with each object interlinked with the information of the specific id. The excel list is used to import all data to OpenDSS.

2.2 OpenDSS

The Open Distribution System Simulator (OpenDSS) is an open source program which specializes in simulation and examination of electrical distribution systems [5]. The program is manly used to analyze voltage, current and power levels, depending on a load. Each object in the system can be defined in OpenDSS with all the attributes included (mainly cable info, the impedance, connection configuration etc.) to make the simulation as close to reality as possible. The connecting points for all the objects in the system are so called busses, a form of connection with input and output source. This make it possible to analyze each part of a system individually, as well the whole circuit, with total losses and power levels etc.

2.3 Electric car charger

There are many different types of charger for electric cars, the main difference is the charging speed [6]. It varies from the fastest DC-chargers made by Tesla (rated 250kW) to the most basic charger directly from the electrical outlet at home which could charge at a rate of 7kW. The tesla charger could technically give a car fully charged battery (battery range of around 500km) in under an hour. It would reach a 50% charged battery in around 10 minutes [7]. These

chargers are not intended for home charging but function more like a conventional gas station and are usually placed close to lager roads.

In this study, home chargers for electric cars are used. They have charging rates adapted to the limited power levels of a household. This study investigates the effect of installing a standard Nissan Leaf charger at home. The charger is limited to a one phase configuration with a power consumption depending on the fuse of the house [1]. With these lower charging rates it would take 7-8h for a car to get fully charged, depending on type of electric car (Battery electric vehicle (BEV) or Plug-in Hybrid electric vehicle (PHEV)). The main difference between electric powered

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3 cars is the battery size, the BEV is fully electric and the PHEV is a hybrid. The BEV have a range between 300-400 km, and the PHEV is limited to a max range of about 50 km. These lower range rated electric hybrid cars will consequently not take as long to charge due to the smaller battery capacity, full charge can be achieved in an hour or two [8].

The charger attributes of the Nissan Leaf charger have been analyzed and noted for harmonics reaching from 3^rd to the 15^th. Harmonics of higher order than 15 have little impact and have been neglected in this study [1]. The harmonic content for the specific Nissan Leaf electric car charger can be found in Table 1.

Table 1: Line current harmonic content of Nissan Leaf charger.

Harmonic order (n) Magnitude (%) Angle (deg)

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

2.4 The Swedish electrical grid

The electrical grid in Sweden consists of different voltage levels, high voltages from the

powerplant which is then transformed to manageable levels near customers connected to the grid. There are 4 main voltage levels used when transmitting power from the power plants, see Figure 1. The first one, main core, with the highest voltage rates, around 220-400 kV, supplies power to the regional and local grids. The main core in the electrical grid consist of around 15000 km of power lines [9]. The next stepdown in the electrical grid is the regional grid, where the voltage have been transformed down to a rate of 20-130 kV. From the regional grid to the local grid, the voltage is stepped down once again to meet the rated level of the local grid, known as the distribution grid. At first the voltage level is lowered to 10-20 kV and then stepped down to between 0.4-10 kV. The voltage levels of the local grids are divided into two parts for consumption, high-voltage and the low-voltage local grid. The high-voltage grid is rated to have a voltage level above 1 kV and the low-voltage part in the distribution grid are rated for voltage levels less or equal to 0.4 kV [10]. The model of the Swedish electrical grid can be seen in Figure 1.

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4 Figure 1: showing the configuration of the electrical grid in Sweden

2.5 Harmonics

The characteristics of a signal depends on the load which is connected to the power source. A linear load will contribute to a signal with a proportional ration between the voltage and current according to Ohm´s law.

𝑉 = 𝐼 × 𝑅 (2.1)

A non-linear load will cause the signal to have non-linear characteristics, thus Ohms law will not apply to these types of signals [11]. The non-linear signals consist of smaller signals with

different frequencies (harmonic distortions), which together will alter the attribute of the base signal. The result of combined signals, due to addition of harmonic distortion can be defined with Fourier series analysis [12].

𝑓(𝑡) = ¹

2𝑎₀+ ∑^∞_ℎ=1𝑎_ℎ𝑐𝑜𝑠(ℎ𝜔𝑡) + 𝑏_ℎ𝑠𝑖𝑛(ℎ𝜔𝑡) (2.2a)

𝑎₀ = ¹

𝜋∫₀^2𝜋𝑓(𝑡) 𝑑𝑡 (2.2b)

𝑎_ℎ = ¹

𝜋∫₀^2𝜋𝑓(𝑡)𝑐𝑜𝑠(ℎ𝜔𝑡)𝑑(𝜔𝑡) ℎ = 1, 2, … . , ∞ (2.2c)

𝑏_ℎ = ¹

𝜋∫₀^2𝜋𝑓(𝑡)𝑠𝑖𝑛(ℎ𝜔𝑡)𝑑(𝜔𝑡) ℎ = 1, 2, … . , ∞ (2.2d)

𝜔 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑡 = 𝑡𝑖𝑚𝑒

ℎ = ℎ𝑎𝑚𝑜𝑛𝑖𝑐 𝑜𝑓 𝑎 𝑠𝑝𝑒𝑠𝑖𝑐𝑖𝑓 𝑜𝑟𝑑𝑒𝑟

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5 The base signal consists of the fundamental frequency, in this case 50Hz which is the standard in the Swedish power grid. All additions to the signal are made up of multiples of the fundamental frequency, i.e. the 3^rd harmonic corresponds to a signal with a frequency of 150 Hz, the 5^th harmonic corresponds to a sinusoidal signal with the frequency 250 Hz and so on, as can be seen in figure 2.

Figure 2: The resulting signal when combining the fundamental frequency with the 3^rd harmonic

The deviation from the fundamental frequency with the addition of harmonic distortion will contribute to losses in a system. In this thesis, the effect of harmonics in power systems are limited to the impact on the transformers.

The main source of losses in cables due to harmonic deviation is dissipated as heat. It is the non- linear harmonic current addition which increase the heat losses, according to the equation 2.3.

As the cable resistance is dependent of the current frequency, deviation from the fundamental frequency thus contributes to the heat loss [13].

𝑃_{ℎ𝑒𝑎𝑡} = 𝐼²× 𝑅_{𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟} (2.3)

Similarly, heat losses appear in transformers when connected to a non-linear harmonic load (Pheat). It is mainly the copper conductors in the transformer coil that contribute to the heat losses, similar to equation 2.3. The copper losses are considered constant, corresponding to the

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6 current drawn by the fundamental frequency through the windings. Together with iron/core losses and stray losses, the copper losses constitute the load loss part of the transformer.

Depending on the part of the transformer affected by the loss, it could be divided further into subcategories. The iron/core loss is due to hysteresis and eddy currents (PEC) which affect the core and windings of the transformer. The electromagnetic flux contributes to stray losses (POSL) which affect the windings and other metallic structural parts in between and around the

windings of the transformer [14]. The increase in harmonic current thought the transformer, due to stray losses will contribute to heat losses in the end[15]. The total load loss in the transformer can be define by equation 2.4.

𝑃_{𝐿𝑜𝑎𝑑−𝑙𝑜𝑠𝑠} = 𝑃_{ℎ𝑒𝑎𝑡(𝐼}²_×𝑅)+ 𝑃𝑖𝑟𝑜𝑛/𝑐𝑜𝑟𝑒(𝐸𝐶)+ 𝑃_{𝑠𝑡𝑟𝑎𝑦(𝑂𝑆𝐿)} (2.4)

From now on focus will be on the eddy current and stray loss effect on the transformer, as they both are affected directly by the addition of harmonics currents.

The eddy current losses affect the windings of the transformer, which can reach high

temperatures due to non-sinusoidal currents. These losses are given by equations 2.5a and 2.5b.

𝑃_𝐸𝐶 = 𝑃_{𝐸𝐶−𝑅} × 𝐾_𝑃𝑒𝑐 (2.5a)

𝐾_𝑃𝑒𝑐 = ∑ ^𝐼^{ℎ𝑟𝑚𝑠}²

𝐼_{𝑓𝑟𝑚𝑠}ℎ²

ℎ𝑚𝑎𝑥

ℎ=1 (2.5b)

𝑃𝐸𝐶𝑅= 𝑛𝑜𝑟𝑚𝑎𝑙 𝑟𝑎𝑡𝑒𝑑 𝑒𝑑𝑑𝑦 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑙𝑜𝑠𝑠𝑒𝑠

𝐼ℎ = 𝑡ℎ𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑜𝑓 𝑎 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑜𝑟𝑑𝑒𝑟 ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐 (𝑅𝑀𝑆) 𝐼𝑓𝑟𝑚𝑠= 𝑡ℎ𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 (𝑅𝑀𝑆)

ℎ = 𝑡ℎ𝑒 ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐 𝑜𝑓 𝑎 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑜𝑟𝑑𝑒𝑟

The remaining stray losses (POSL) contribute to the losses in the core part of the transformer.

The harmonic currents will contribute to temperature rise in the structural parts of the

transformer and thus increase the heat losses. The stray losses are given by equations 2.6a and 2.6b.

𝑃_𝑂𝑆𝐿 = 𝑃_{𝑂𝑆𝐿𝑅} × 𝐾_𝑂𝑆𝐿 (2.6a)

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𝐾_𝑂𝑆𝐿 = ∑ ^𝐼^ℎ²

𝐼_{𝑓𝑟𝑚𝑠}ℎ^0,8

ℎ𝑚𝑎𝑥

ℎ=1 (2.6b)

𝑃_{𝑂𝑆𝐿𝑅}= 𝑛𝑜𝑟𝑚𝑎𝑙 𝑟𝑎𝑡𝑒𝑑 𝑠𝑡𝑟𝑎𝑦 𝑙𝑜𝑠𝑠𝑒𝑠

𝐼_ℎ = 𝑡ℎ𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑜𝑓 𝑎 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑜𝑟𝑑𝑒𝑟 ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐 (𝑅𝑀𝑆) 𝐼𝑓𝑟𝑚𝑠= 𝑡ℎ𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 (𝑅𝑀𝑆)

ℎ = 𝑡ℎ𝑒 ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐 𝑜𝑓 𝑎 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑜𝑟𝑑𝑒𝑟

Out of the total rated load loss the 𝑃_{ℎ𝑒𝑎𝑡(𝐼}²_×𝑅) part will be around 75%, 𝑃_{𝐸𝐶−𝑅} about 15%

and 𝑃_{𝑂𝑆𝐿𝑅} about 10% [14]. These percentage values are estimates for a 5000 kVA transformer.

The transformers implemented in the electrical grid of this study have a lower power rating.

However, the proportion for each loss is assumed to follow a similar pattern, where 𝑃_{ℎ𝑒𝑎𝑡(𝐼}²_×𝑅) will constitute the largest part of the total loss, while 𝑃_{𝐸𝐶−𝑅} and 𝑃_{𝑂𝑆𝐿𝑅} will be significantly lower.

The winding configuration of the transformers, delta to wye, will also contribute to some losses due to the harmonics. The primary part with a delta configuration will isolate the 3^rd harmonic, as there is no mutual joint between the tree phases. The harmonic currents will circulate in the delta configuration, and cause some overheating problems in the windings, as it cannot

propagate to the secondary side of the transformer [13].

The harmonic effects on the power system can be define by looking at the total harmonic distortion and by examining the percentage of each individual harmonic. There are guidelines, set by The Swedish Energy Market Inspectorate, to ensure a stable electrical grid to consumers.

The total harmonic distortion (THDU) for voltages is limited to 8% and the limits for each individual harmonic is shown in Table 2 [3]. The total harmonic distortion value for voltages is given by equation 2.7.

𝑇𝐻𝐷_𝑈 =^√∑ ^𝑼^𝒉

𝟐

∞𝒉=𝟐

𝑼𝒇𝒖𝒏𝒅𝒂 (2.7)

𝑈ℎ= 𝑡ℎ𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎 𝑠𝑝𝑒𝑠𝑖𝑓𝑖𝑐 𝑜𝑟𝑑𝑒𝑟 ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐 𝑈𝑓𝑢𝑛𝑑𝑎 = 𝑡ℎ𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 ℎ =harmonic of a specific order

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8 The distortion for the individual harmonics (THDindiv) is the percentage between the

fundamental frequency and a specific harmonic distortion according to equation 2.8.

𝑇𝐻𝐷_{𝑖𝑛𝑑𝑖𝑣}= ^𝑈^ℎ

𝑈𝑓𝑢𝑛𝑑𝑎× 100 (2.8)

𝑈_ℎ= 𝑡ℎ𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎 𝑠𝑝𝑒𝑠𝑖𝑓𝑖𝑐 𝑜𝑟𝑑𝑒𝑟 ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐 𝑈_{𝑓𝑢𝑛𝑑}= 𝑡ℎ𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

Table 2: Individual voltage harmonic levels set by The Swedish Energy Market Inspectorate

Odd Harmonics Even Harmonics

Not multiple of 3 Multiple of 3 Harmonics

(n)

Individual harmonic limits (%)

Harmonics (n)

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…… 24 0.5 %

13 3.0 % 21 0.5 %

17 2.0 %

19 1.5 %

23 1.5 %

25 1.5 %

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9

3 Method

3.1 Implemented methods

The maps provided by the electric company were displayed using the QGIS program. All the connection points for the transmission wires and consumers were extracted and used to model the electrical grid in the simulation program OpenDSS.

The main study was conducted in the simulation program OpenDSS. The simulations were based on the highest power demand during one day. It was a static simulation study, where a specific point in the electrical grid was monitored. In this case, the transformers of both areas were studied to see the effects of added harmonics. A 24 h load profile, provided by the electric company, was used to define the maximum load for each household during one day. This value was set as the main load for each customer connected to the grid. The electric car charger was then added to the total load of each household. The additional load was defined, including the harmonics, using data for a 1-phase charger provided in [1].

With the added harmonic content to the load a static power flow simulation was performed.

Further the harmonic flow analysis was implemented to solve for each added harmonic, including voltage and current harmonic distortion values in the monitored transformer.

To compile and visualize the results all simulated data, including all voltage and current harmonic values, were exported to Excel.

To summarize, the electrical car charger was added as an extra load to all households in both the studied areas. The number of connected chargers was increased gradually from 10% - 100%.

The study was made with two different load configuration, all additional loads connected to the first phase of each household compared to all additional loads distributed evenly on three phases.

3.2 Power grid

The power grid of two different areas was analyzed using data provided by the electric company Dala Energi. One area had a weaker grid than the other. Both areas are connected to the main overhead transmission line at a voltage level of 10kV, the voltage level is then transformed to a customer standard of 0.4kVLL. The first area, A, contained 154 customers and the second area, B, around 170 customers connected to the low-voltage grid. Most of the low-voltage cables in area A are placed underground, in Area B there is a mix of both underground cables as well as a few overhead transmission lines.

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10 Figure 3: The map of the electric grid in Area A

Figure 4: The map of the electric grid in Area B

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11

3.2 OpenDSS programming

The data provided by Dala Energi was examined in the QGIS simulation program. From the maps, all the attributes for cables and transformers were exported to excel sheets. The required data to define lines in OpenDSS was the length, number of phases, positive and negative

sequence resistance, reactance, capacitance and the bus configuration, starting and end point.

Example of the line defining a cable in OpenDSS is seen below.

The OpenDSS code below defines lines in the area:

New Line.1883276 bus1=1891108.1.2.3.4 bus2=1883277.1.2.3.4 length=20.605 units=m Linecode=EKKJ1010 New Linecode.EKKJ1010 nphases=4 R1=1.83 X1=0.091106187 R0=1.83 X0=0.091106187 C1=320 C0=320 units=km

The transformers located in the electric substations of the two areas, was defined as well. All the transformers were rated to transform the voltage from 10 to 0.4kV on the secondary side.

The connection configuration was the same for all the transformers, delta on the primary winding side and wye connection on the secondary winding side. Each side, primary and

secondary, were defined as well as the windings and phases. The primary side was connected to the source bus, which corresponded to a connection to the high-voltage transmission lines with a 10kV voltage level. The secondary side was connected to a bus, where the lower voltage level of 0.4kV was distributed to other parts of the area.

The OpenDSS code below defines transformers in the area:

New Transformer.T5442 phases=3 windings=2

~ wdg=1 bus=sourcebus kV=11 kva=100 conn=delta

~ wdg=2 bus=1958318.1.2.3.4 kV=0.4 kva=100 conn=wye

The loads were divided into main and additional load from the electric car charger, where the main was the base consumption of the household excluding the electric car charger. Each customer connected to the grid in the area were modelled as a 3-phase load. The power value of the load was chosen from a daily power consumption graph, actual 24h values from one of the households in the area, shown in Figure 5. The car is assumed to be charged during the night at home. Thus, an average value is calculated for the power consumption during the time when the car is charging. The power consumption value is calculated to be 3 kW and is used when defining each household in the grid as a load.

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12 Figure 5: 24h power consumption from a customer in the area

The same power consumption of 3kW was applied to each customer in the grid as the main load. Hence, the main load was defined as a 3-phase wye configuration load with a power factor of 0.95. The value of the power factor is determined by the electrical devices in the household [2].

The OpenDSS code below defines the main loads in the area:

New Load.Load2000992 Bus1=2000992.1.2.3.4 kV=0.4 kW=3 pf=0.95 Phases=3 conn=wye

The electric car charger was modeled as a 1-phase load with specific harmonic attributes that will affect the power grid [1]. The electric car charger used in this study was limited to a max charging rate of 6.6 kW [1]. Thus, the current limit for each household (i.e. the fuse) was used to define the 1-phase charger as a harmonic load. The connecting point used to define the main load for each household was also used to connect the extra harmonic load. Each household has a main fuse, which limits the amount of power the charger can utilize, ranging from 16 to 25 ampere. Depending on the fuse limit, the power consumption used to charge the car varies for each household.

The OpenDSS code below defines the harmonic loads in the area:

New Spectrum.NissanLeafCharger

~ Numharm=8

~ Harmonic=[1, 3, 5, 7, 9, 11, 13, 15]

~ %mag=[100 25 17 14.2 9.69 5.04 1.8 0.37]

~ Ang=[-26 -94 -96 -72 -68 -49 -49 -46]

New Load.HarmonicLoad2001049 Bus1=2001049.1.4 kV=0.230 pf=0.98 Phases=1 Spectrum=NissanLeafCharger kVA=4.6

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13 As this study analyzed the instantaneous effect of harmonics, the power consumption from the harmonic loads were kept unchanged during the simulation. The only difference between the simulations were the placement of the 1-phase loads. Either they were all connected to the first phase or they were evenly distributed between all three phases.

The OpenDSS code below defines the load configuration:

Bus1=2001049.1.4 first phase and ground configuration Bus1=2001049.2.4 second phase and ground configuration Bus1=2001049.3.4 third phase and ground configuration in the circuit

All the components, lines, transformers and both loads, were defined separately. Then they were all called from a main script to simulate the whole grid of the area. A new circuit was defined with a fundamental frequency of 50 Hz and a voltage source to supply the power of the circuit. The source voltage was set to a corresponding standard impedance of (0,1 + j1 )Ω [16].

The OpenDSS code below defines the source voltage in the area:

Edit VSource.source BasekV=10 pu=1.05 ISC3=5800 corresponds to a10kV impedance of R1=0.1 X1=1

The complete OpenDSS code for area B can be found in Appendix A

3.4 Simulation in OpenDSS

When the whole grid was defined, the harmonic mode simulation applied the effect of the harmonic loads to the grid. In order to analyze a specific part of the grid, a monitor was set to specify where the result should be extracted from. In this case the transformers were the focus of the simulations. The effect of harmonics on the grid was examined with different

configurations of the harmonic loads. The results come as text files, which was converted to excel format in order to compile the values into tables and graphs. The table consisted of voltage and current values for each harmonic effecting the specific transformer. These values were then used to calculate THDU (eq. 2.7) and individual distortion values for each harmonic (eq. 2.8) up to the 15^th order. The losses in the transformer due to harmonic currents was calculated with, eq. 2.5b and 2.6b. The first phase was used as a reference when the effect of the harmonics was compared against a load where all three phases are utilized. These

parameters were calculated for the two different harmonic configurations, all loads on the same phases versus the mixed dispersion, for both areas A and B. Each result was calculated with a load on the grid ranging from 10% customers with car chargers to 100% customers in the area with a harmonic load connected to the household.

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14

4 Results

OpenDSS was used to simulate how harmonic loads affects the transformer of the electrical grid in two areas, A and B. The harmonic load was increased stepwise from 10% to 100%, the same simulations were made for the electrical grid of both A and B. In total there was 10 tables produced to analyze the effect when increasing the load on the area with 10% each time. The tables include a list of harmonics and their corresponding frequency value, ranging from 1^st to 15^th harmonic deviation of the fundamental frequency. These tables were produced for both the areas with two different configurations of the load placement in the 3-phase grid, first phase versus a mixed dispersion.

The simulated data is presented in graphs (figures 6-12 for area A and figures 16-22 for area B) to illustrate harmonic distortion ratio for both connection configuration. The limits set by The Swedish Energy Market Inspectorate, i.e. how much each harmonic is allowed to affect the grid, was added to the graphs to show the amount of load the grid could handle before exceeding the limits.

The simulate results were then used to calculate the total harmonic distortion for the voltage in each transformer in area A and B. The results were compiled in graphs (figure 13 for area A and figure 23 for area B) showing the total harmonic distortion level for each load percentage. Both configurations were included in the same graph to analyze the difference in impact.

The current level for each harmonic distortion was used to calculate two different loss factors, eddy current and stray losses, due to the harmonic currents in the transformer. Both were compiled in individual graphs (figures 14/15 for area A and figure 25/ 25 for area B) which show how the p.u. loss factor increase when the load from the car chargers was added to the areas.

4.1 Area A results

The results are the outcome from simulation made with OpenDSS. In addition to the two different areas, simulations were made to analyze different connections of the harmonic loads to the 3-phase grid, load limited on the first phase versus distributed evenly on all three phases.

In all simulations the results contained data of voltage and current values for each added harmonic ranging from the 1^st to the 15^th.

The results for Area A are shown in tables and graphs below.

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15 Table 3a: voltage and current values for each harmonic, with 10% of the households connected to an

extra harmonic load, first phase configuration.

10% Harmonic Load in Area A, first phase

Freq [Hz] Harmonic (n) V1 [V] V1Angle1 [°] I1 [A] I1Angle1 [°]

50 1 238,021 -32,6432 473,527 131,284

150 3 2,42069 113,895 32,9964 25,5343

250 5 2,68148 73,6661 21,8996 -15,1737

350 7 3,09344 59,3508 17,9879 -29,6349

450 9 2,68932 24,9191 12,1051 -64,0828

550 11 1,69756 5,40126 6,21238 -83,5402

650 13 0,712279 -33,171 2,1881 -121,991

750 15 0,168101 -68,7778 0,443165 -157,418

Table 3b: voltage and current values for each harmonic, with 100% of the households connected to an extra harmonic load, first phase configuration.

100% Harmonic Load in Area A, first phase

50 1 225,745 -39,951 1783,02 126,995

150 3 19,7697 75,6429 270,808 -12,64

250 5 19,6847 16,7661 161,552 -71,9103

350 7 21,0103 -14,7849 122,775 -103,529

450 9 17,1451 -66,0447 77,5588 -154,727

550 11 10,225 -102,145 37,6107 169,311

650 13 4,06748 -157,054 12,5613 114,605

750 15 0,912329 151,259 2,41859 63,1817

For voltages and current values for harmonic load between 10% and 100% is see appendix A Table 4a: voltage and current values for each harmonic, with 10% of the households connected to an

extra harmonic load, all three phases utilized.

10% Harmonic Load in Area A, 3-phases utilized

50 1 238,865 -32,0713 361,077 131,2

150 3 0,632891 122,191 9,43791 34,0403

250 5 0,862333 80,3382 5,88573 -6,89436

350 7 0,999088 66,0713 4,91837 -21,4933

450 9 0,758042 33,1803 3,62947 -54,6102

550 11 0,551879 15,0968 1,7329 -73,1703

650 13 0,230241 -22,5592 0,614947 -111,428

750 15 0,051347 -58,6629 0,135333 -144,81

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16 Table 4b: voltage and current values for each harmonic, with 10% of the households connected to an

extra harmonic load, all three phases utilized.

100% Harmonic Load in Area A, 3-phases utilized

50 1 234,892 -34,5586 811,23 130,265

150 3 6,62524 103,955 100,141 15,6354

250 5 8,37027 57,222 66,8359 -32,176

350 7 9,2618 37,5763 52,6672 -52,0676

450 9 7,17418 0,121338 34,953 -87,8993

550 11 4,89697 -25,7904 17,7873 -115,672

650 13 1,97575 -68,5527 6,03264 -158,622

750 15 0,455505 -108,318 1,23489 165,301

The voltages and current values for harmonic load between 10% and 100% are presented in appendix A

4.1.1 Individual harmonic distortion

The harmonic distortion for individual harmonics was calculated with eq. 2.8, using values from tables 3a and 3b. Figure 6 below show the harmonic distortion voltage level for each individual harmonic in Area A, ranging from 3^rd to 15^th order.

Figure 6: The 3^rd voltage harmonic distortion level

0 2 4 6 8 10

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Percentage load an the area

Area A 3rd voltage harmonic distortion %

Mixed dispersion

Approved level for the 3rd voltage harmonic First phase configuration

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17 Figure 7: The 5^th voltage harmonic distortion level

Figure 8: The 7^th voltage harmonic distortion level

0 2 4 6 8 10

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Percentage load on the area

Area A 5th voltage harmonic distortion %

Mixed dispersion

Approved level for the 5th voltage harmonic First phase configuration

0 2 4 6 8 10

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Area A 7th voltage harmonic distortion %

Mixed dispersion

0 2 4 6 8

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Area A 9th voltage harmonic distortion %

Mixed dispersion

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0 1 2 3 4 5

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Area A 11th voltage harmonic distortion %

Mixed dispersion

0 1 2 3 4

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Area A 13th voltage harmonic distortion %

Mixed dispersion

Approved level for the 13th voltage harmonic

First phase configuration

0 0,2 0,4 0,6

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Area A 15th voltage harmonic distortion %

Mixed dispersion

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19 4.1.2 THDU

Equation 2.7 was used to calculate the total harmonic distortion for the voltage level in the transformer of Area A. The results are shown in figure 13 below.

Figure 13: The total voltage harmonic distortion (THDU) in a transformer of the Area A, with two different configurations

4.1.3 Eddy current loss

Equation 2.5b was used to calculate the K-factor of the load in Area A, from a 10% load to a full 100% load. The current for each harmonic, found in Tables 4/3, are used for calculating the losses.

Figure 14: The K-factor for the eddy current loss in the transformers of the Area A, with both configurations

0 5 10 15 20

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

THD%

Area A THD

_U

of the tranformer

THDv mixed dispersion

THDv limit

THDv first phase configuration

0 0,5 1 1,5 2 2,5

K-factor p.u

Area A K-factor, eddy current loss in transformer

First phase configuration Mixed dispersion

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20 4.1.4 Stray loss

The remaining stray losses were calculated with equation 2.6b and visualized, with the K-factor for the harmonic load in Area A, in figure 15 below.

Figure 15: The K-factor for the stray loss in the transformers of the Area A, with both configurations

0,9 0,95 1 1,05 1,1 1,15

K-factor p.u

Area A K-factor, stray loss in transformer

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21

4.2 Area B results

The result was the outcome from the simulation made with OpenDSS on the grid for both areas.

In addition to the two different grid areas, simulations were made to analyze different

connections to the 3-phase grid, load exclusive on the first phase versus spread out on all three phases. In all simulations the results containing data of voltage and current values for each added harmonic ranging from the 1^st to the 15^th.

The results for Area B were compiled in tables and graphs below.

Table 5a: voltage and current values for each harmonic, with 10% of the households connected to an extra harmonic load, first phase configuration.

10% Harmonic Load in Area B, first phase

50 1 221,822 -31,0687 29,6138 -163,149

150 3 1,88507 135,391 4,17312 59,6136

250 5 2,31161 88,3064 3,19512 9,11499

350 7 2,77971 69,8188 2,80374 -11,0392

450 9 2,46498 32,3816 1,9556 -49,5097

550 11 1,56923 10,4902 1,02332 -72,077

650 13 0,659333 -30,0528 0,363788 -113,05

750 15 0,155041 -67,346 0,07386 -150,583

Table 5b: voltage and current values for each harmonic, with 100% of the households connected to an extra harmonic load, first phase configuration.

100% Harmonic Load in Area B, first phase

50 1 215,632 -36,1233 175,366 142,538

150 3 13,7816 93,4645 36,5337 8,95436

250 5 14,3428 39,327 23,1803 -44,3451

350 7 15,4444 12,6212 17,978 -70,0506

450 9 12,4539 -33,6062 11,3124 -115,134

550 11 7,22537 -64,4948 5,36816 -144,7

650 13 2,75871 -114,02 1,72923 167,321

750 15 0,586499 -160,161 0,317114 123,005

The voltages and current values for harmonic load between 10% and 100% is are presented in appendix A

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22 Table 6a: voltage and current values for each harmonic, with 10% of the households connected to an

extra harmonic load, all three phases utilized.

10% Harmonic Load in Area B, 3-phases utilized

50 1 221,622 -30,7519 23,0864 -163,971

150 3 0,574174 128,655 0,850234 71,4358

250 5 0,79134 101,734 1,36752 14,3622

350 7 0,899149 69,3613 1,01353 -17,7725

450 9 0,729448 33,7137 0,462735 -35,7445

550 11 0,535336 24,6379 0,410368 -65,1045

650 13 0,205745 -23,5133 0,127736 -111,764

750 15 0,048092 -60,7335 0,018337 -133,629

Table 6b: voltage and current values for each harmonic, with 100% of the households connected to an extra harmonic load, all three phases utilized.

100% Harmonic Load in Area B, 3-phases utilized

50 1 220,809 -32,1484 55,0813 163,351

150 3 4,04812 117,242 9,98884 38,2431

250 5 5,53925 72,1305 8,33481 -11,2795

350 7 6,65437 54,9953 7,06108 -34,4739

450 9 4,7914 11,9992 4,29127 -61,0885

550 11 3,42018 -8,67162 2,39104 -93,4144

650 13 1,43783 -49,1085 0,833678 -139,312

750 15 0,292484 -94,8801 0,151821 -161,622

The voltages and current values for harmonic load between 10% and 100% are presented in appendix A

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23 4.2.1 Individual harmonic distortion

The harmonic distortion for individual harmonics was calculated with equation 2.8, using values from tables 5a and 5b. Figures 16 to 22 below shows the harmonic distortion voltage level for each individual harmonic in Area B, ranging from the 3^rd to the 15^th harmonic.

Figure 16: The 3^rd voltage harmonic distortion level

0 2 4 6 8

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Area B 3rd voltage harmonic distortion %

Mixed dispersion

Approved level for the 3rd voltage harmonic First phase configuration

0 2 4 6 8

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Area B 5th voltage harmonic distortion %

Mixed dispersion

0 2 4 6 8

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Area B 7th voltage harmonic distortion %

Mixed dispersion

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0 2 4 6 8

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Area B 9th voltage hamronic distortion %

Mixed dispersion

0 1 2 3 4

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Area B 11th voltage harmonic distortion %

Mixed dispersion

0 1 2 3 4

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Distortion level %

Area B 13th voltage harmonic distortion %

Mixed dispersion

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4.2.2 THDU

Equation 2.7 was used to calculate the total harmonic distortion for the voltage level in the transformer of Area B. The results are shown in figure 23 below.

Figure 23: The total voltage harmonic distortion (THDU) in a transformer of the Area B, with two different configurations

4.2.3 Eddy current loss

Equation 2.5b was used to calculate the K-factor the load in Area B, from a 10% load to a full 100% load. The current for each harmonic, presented in Table 5 and 6, was used to calculate the losses.

0 0,1 0,2 0,3 0,4 0,5 0,6

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

DIstortion level %

Area B 15th voltage harmonic distortion %

Mixed dispersion

0 5 10 15

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

THD%

Area B THD

_U

of the transformer

THDv mixed dipersion

THDv limit

THDv first phase configuration

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26 Figure 24: The K-factor for the eddy current loss in the transformers in the Area B, with both

configurations

4.2.4 Stray loss

The remaining stray losses for the harmonic load in Area B were calculated with equation 2.5b and are visualized with the K-factor in figure 25 below.

Figure 25: The K-factor for the stray loss in the transformers of the Area B, with both configurations

0 1 2 3 4

10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

K-factor p.u

Area B K-factor, eddy current loss in transformer

0 0,2 0,4 0,6 0,8 1 1,2 1,4

K-factor p.u

Area B K-factor, stray loss in transformer

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27

5 Discussion

The effects of harmonic distortion on the electrical grid analyzed in this thesis are limited to attributes of the specific electric car charger used as added load to the consumers in both areas.

It could furthermore be examined with other types of electric car chargers to get a deeper understanding of how harmonic distortion from car chargers affects the electrical grid.

5.1 THD results analysis

The results regarding the THD follow a similar pattern for both areas, where the individual harmonic distortion is kept within limits by changing the phase configuration of one phase car charger. When all the chargers are connected to the same phase, some of the individual

harmonic distortion exceed the limit when 50-60% of the customers in the area are loaded with the harmonic load.

The only exception is the 9^th harmonic, in both configurations the limit is exceeded. However, it is greatly reduced when spread to all three phases in the area, from a 10% harmonic load to about 40-50% harmonic load on the consumers connected to the electrical grid of the area. The effect of the 9^th harmonic distortion could be reduced to acceptable levels by adding a filter to the grid or directly to the electric car charger.

The total harmonic voltage distortion of the transformers in both areas show a similar pattern of reduction, when switching between both load configurations. The 8% limit is surpassed at around 40% load for both areas in the first phase configuration, while a mixed dispersion

enables a 100% load in each area without surpassing the limit set by The Swedish Energy Market Inspectorate [3].

The percentage of THD also depends on the total base power consumption in the area. For example, if the total power consumption on the transformer is 100kW and the total harmonic distortion corresponds to 1kW, it will be 1% harmonics distortion of the total power

consumption. If the base consumption would decrease to half power consumption, 50kW, and the harmonic distortion from chargers would remain at 1kW the total percentage would increase to 2% for the harmonic distortion. Consequently, the total harmonic limit of 8% is exceeded earlier if the main base consumption is lower and the harmonic load stays the same.

Thus, it is important to strive for a well-balanced, dimensioned and rated transformer to maintain THD as leveled as possible.

5.2 Eddy current loss results analysis

The eddy current loss results differ between both areas, area A seem to have a gradual increase of the loss factor, K, when adding the load. The first phase configuration reaches a factor 2 at around 50% load, while the configuration with a mixed dispersion have a more linear increase, towards a factor 2 loss at around 100% load in the area.

The same load analysis on the eddy current loss for the transformer in Area B results in a higher loss factor. Additionally the first phase configuration seem to have some unforeseen results, where the loss factor K oscillates around a factor 3. On the other hand, the results of the mixed

The Effect of Harmonics on the Electrical Grid due to Electric Vehicle Chargers _____________________________

The Effect of Harmonics on the

Electrical Grid due to Electric Vehicle Chargers

_____________________________

Ingemar Solander Araúz

Bachelor Thesis 15hp

December 2020

Abstract

The Effect of Harmonics on the Electrical Grid due to Electric Vehicle Chargers

Popular science summary

Exekutiv sammanfattning

Acknowledgements

Contents

1 Introduction

2 Theory

3 Method

4 Results

Area A 3rd voltage harmonic distortion %

Area A 5th voltage harmonic distortion %

Area A 7th voltage harmonic distortion %

Area A 9th voltage harmonic distortion %

Area A 11th voltage harmonic distortion %

Area A 13th voltage harmonic distortion %

Area A 15th voltage harmonic distortion %

Area A THD

of the tranformer

Area A K-factor, eddy current loss in transformer

Area A K-factor, stray loss in transformer

Area B 3rd voltage harmonic distortion %

Area B 5th voltage harmonic distortion %

Area B 7th voltage harmonic distortion %

Area B 9th voltage hamronic distortion %

Area B 11th voltage harmonic distortion %

Area B 13th voltage harmonic distortion %

Area B 15th voltage harmonic distortion %

Area B THD

of the transformer

Area B K-factor, eddy current loss in transformer

Area B K-factor, stray loss in transformer

5 Discussion