• No results found

Power quality in low voltage grids with integrated microproduction

N/A
N/A
Protected

Academic year: 2022

Share "Power quality in low voltage grids with integrated microproduction"

Copied!
49
0
0

Loading.... (view fulltext now)

Full text

(1)

ES10026

Examensarbete 30 hp December 2010

Power quality in low voltage

grids with integrated microproduction

mårten einarsson

(2)

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

Power quality in low voltage grids with integrated mircroproduction

mårten einarsson

This report seeks to evaluate and predict possible power quality issues regarding Fortums engagement in the project of Stockholm Royal Seaport. Stockholm Royal Seaport is a city district planned by Stockholm Municipality to be constructed based on sustainable urban city principles. Fortum has, together with additional partners, engaged in the challenge to create a sustainable energy system.

This is thought to be achieved through several measures. Energy saving actions are in-corporated at several levels and there is a plan to create a “smart grid” for the electricity supply. A smart grid has no strict definition but in this case a key feature is

“demand-response” which effectively means a way to optimize the consumption to have a more balanced consumption over the 24 hours of a day.

One of the key components in the smart grid is the “active house” which is planned to have several specific features separating it from an ordinary house. It is planned to have its own contribution to electricity production using solar cells and an energy storage using batteries. Another feature is thought to be both automation and economic incentives measures to achieve peak load reduction.

This thesis has taken the perspective of the end customer in the active house and has tried to evaluate the power quality to be experienced. An investigation regarding the dif-ferent components has been carried out to get an overview from the mentioned perspective and identify possible problems or issues that may require attention in the realization of Stockholm Royal Seaport.

It has been found that no major problems are to be expected but some smaller issues has arisen that might be worthwhile giving some attention.

Examinator: Kjell Pernestål Ämnesgranskare: Mats Leijon

Handledare: Jan-Olof Olsson, Johan Lundin

(3)
(4)
(5)

Sammanfattning

Den här rapporten syftar till att evaluera och förutspå eventuella elkvalitetsproblem för Fortums engagemang i projektet Norra Djurgårdsstaden. Norra Djurgårdsstaden är en stadsdel i Stockholm planerad av Stockholms stad i hållbarhetens tecken. Fortum har, till- sammans med ytterligare aktörer, engagerat sig i att skapa ett hållbart energisystem.

Detta är tänkt att uppnås genom flera åtgärder. Energibesparingsåtgärder utförs på flera plan och man tänker sig implementera ett koncept man kallar ”smarta nät” för elförsörj- ningen. Ett smart nät kan definieras på flera olika sätt men här handlar det mycket om att styra elkonsumtion för att uppnå en jämnare elförbrukning över dygnet.

En av baskomponenterna i det tänkta smarta nätet är det ”aktiva huset” som planeras ha ett antal speciella egenskaper jämfört med ett ordinärt hus. Man tänker sig egen elproduk- tion i form av solceller samt energilagring med hjälp av batterier. Man tänker sig också olika former av mjuka och hårda styrmedel för att kontrollera elkonsumtion.

Examensarbetet har utgått från slutkund i det aktiva huset och har sökt utvärdera vad denne kommer att uppleva i form av elkvalitet. Man har tittat på de olika komponenterna för att bilda en helhetsuppfattning ur det givna perspektivet och identifiera eventuella pro- blem eller frågeställningar som kräver uppmärksamhet inför genomförandet av projektet Norra Djurgårdsstaden.

Examensarbetet har börjat med att definiera begreppet elkvalitet som utgångspunkt. Det är väldigt vagt formulerat i svensk lagstiftning utan grundar sig på branschpraxis som utgår ifrån ett antal europeiska standarders. Vidare förs en diskussion om vem och vad som på- verkar elkvaliteten i nätet.

Därefter görs en grov ekonomisk uppskattning kring problem orsakade av elkvaltetsfe- nomen. Olika rapporter från forskningsorganet Elforsk har gåtts igenom och citeras på uppgifter kring samhällsmässiga, företagsmässiga och privata utgifter i relaterade till dålig elkvalitet.

Det görs sedan en mer teknisk utvärdering av problemet. Här börjar man i den tilltänkta applikationen, solceller, för att ta reda på vilka elektriska egenskaper denna har. Dessa egenskaper har sedan tagits som mall för att utvärdera möjliga elkvaltetsproblem uppkom- na i Norra Djurgårdsstaden.

Man har funnit att det inte väntas uppkomma några större problem men har identifierat några punkter som kan komma att kräva lite noggrannare övervägning.

Nyckelord: elkvalitet, lågspänningsnät, solceller, mikroproduktion, smarta elnät, Norra

Djurgårdsstaden

(6)
(7)

Innehållsförteckning

1 Background 10

1.1 Stockholm Royal Seaport ... 10

1.2 Actors and research goals ... 10

1.3 Distributed generation ... 11

1.4 This thesis relation to the over all goal ... 11

2 Theory 12 2.1 The power grid of today ... 12

2.2 Future grid ... 12

2.3 Motivation to a Power Quality study ... 13

2.3.1 Voltage drop ... 13

2.3.2 Less traditional loads ... 15

2.3.3 Phase asymmetry ... 15

3 Power Quality 16 3.1 General and definition ... 16

3.2 A brief description of the phenomena [V] ... 17

3.2.1 Outage... 17

3.2.2 Frequency variations ... 17

3.2.3 Phase angle ... 17

3.2.4 Transients ... 17

3.2.5 Harmonics ... 17

3.2.6 Voltage variations ... 17

3.2.7 Flicker ... 18

3.2.8 Asymmetry ... 18

3.3 Regulations and Guidelines ... 18

3.4 Official documents ... 18

3.5 Crude guidelines ... 19

3.6 Actual threshold values ... 19

3.7 Comments to EN 50160 ... 21

4 Dangers and implications of bad power quality 22 4.1 Fortums distributing role ... 22

4.2 Protection ... 22

4.3 Common customer damage claims ... 23

4.4 A theoretical example ... 24

4.5 Costs related to power quality on a national scale ... 24

4.6 Discussion about power quality costs ... 25

4.7 Good power quality is sought ... 26

5 Solar cells 28 5.1 History ... 28

5.2 Functionality ... 28

5.3 Electrical characteristics ... 29

5.4 Output of power ... 32

(8)

6 Other components in Stockholm Royal Seaport 33

6.1 General ... 33

6.2 PV generation and batteries ... 33

6.3 Electric cars ... 34

7 Detailed descriptions of PQ phenomena and its effects 36 7.1 Outage ... 36

7.1.1 Outages in Stockholm Royal Seaport ... 37

7.2 Frequency variations... 37

7.2.1 Frequency deviations in Stockholm Royal Seaport ... 38

7.3 Phase angle ... 38

7.3.1 Phase angle in Stockholm Royal Seaport ... 38

7.4 Transient over voltages... 38

7.4.1 Transients in Stockholm Royal Seaport ... 39

7.5 Harmonics ... 39

7.5.1 Harmonics in Stockholm Royal Seaport ... 40

7.6 Voltage variations ... 40

7.6.1 Swells ... 41

7.6.2 Dips ... 41

7.6.3 Current transients ... 41

7.6.4 Voltage variations in Stockholm Royal Seaport ... 42

7.7 Flicker ... 42

7.7.1 Flicker in Stockholm Royal Seaport ... 43

7.8 Asymmetry ... 43

7.8.1 Asymmetry in Stockholm Royal Seaport ... 44

7.9 Summary ... 44

8 Conclusions 46

Acknowledgements 49

(9)
(10)

1 Background

1.1 Stockholm Royal Seaport

Stockholm municipality has taken an initiative to carry out a large scale replanning of a city district through an organization called Stockholm Innovation. This district is located around Hjorthagen and Värtahamnen and the project goes under the name Stockholm Royal Seaport.

The main focus of this new city district revolves around sustainable urban solu- tions. The project is part of Clinton Climate Initiative which is a cooperation be- tween 40 cities across the world to reduce greenhouse gases emissions. The CCI acts as a forum for the participants to exchange experiences in order to promote advances within the field 1 .

1.2 Actors and research goals

Together with ABB, Fortum has joined the project from its position as leading provider of electricity and heat. The idea is to create a full scale test site for a con- cept called “smart grid” that is looked upon as very promising in the struggle to fight climate change. There is no strict definition of what a smart grid is but gener- ally all mentioned properties of a smart grid refer to different ways to optimize electricity generation, transmission and consumption in a smart way. A key feature of the smart grid planned for Stockholm Royal Seaport is the utilization of demand – response technology. This effectively means that one wants to smoothen out the power consumption over a 24 hour horizon, e.g. decrease consumption peaks and move consumption to times when consumption is lower. This is also thought to be achieved through energy storage[II].

1

www.clintonfoundation.org, march 2010

(11)

1.3 Distributed generation

Another aspect of Fortums involvement in the Stockholm Royal Seaport project is the addition of micro production of electricity. For the specific case of Stockholm Royal Seaport, this means electricity production from solar cells. This project is supposed to be a forerunner of things to come. There are strong indications that the electrical environment is about to change from its traditional layout to a much more diversified system with new components to take into account. Small scale production units, connected in locations where the grid was not originally de- signed to connect them, is such a thing. This is generally a widely accepted way to reach goals of renewable energy input set up by both Swedish authorities and European guidelines.

1.4 This thesis relation to the over all goal

The goal of this thesis project has been to look at what can be expected to be the

implications of such a change in the providing electrical system from the end cus-

tomers point of view. The focus will be on power quality, what problems can be

expected, how harmful these problems are expected to be and how to address

them.

(12)

2 Theory

2.1 The power grid of today

The distribution network of tradition is built up around big powerful production units. These units generate onto a core grid that transports the power in high volt- age to the different consumers. Some industrial consumers that are heavy power consumers are connected to the grid on the high voltage side and a regular domes- tic consumer is typically connected at the low voltage side.

Fig 1. Schematic view of traditional power gridFel! Hittar inte referenskälla.

2.2 Future grid

The trend within the electricity sector is pointing towards a more diversified grid

concept. It is expected that the future grids will be more diversified in both genera-

tion and consumption[II]. This is a feature of the subtle expression “smart grids”.

(13)

Substation

User 240V

230V

Substation

User 230V

220V

Fig 3. Voltage upped at the substation to meet demand

This thesis takes aim at providing a small piece of the puzzle in exploring how distributed generation can affect the power quality in the low voltage grid. The thesis is generally focused a bit more on solar power generation but as we will see later on, the conclusions draws can be applied to other power sources.

Fig2. Schematic view of a more diversified expected future power gridFel! Hit- tar inte referenskälla.

2.3 Motivation to a Power Quality study

Why, then, should any problems with power quality be expected approaching this future view of the grid? Below follows a theoretical example and other reasoning intended to illustrate how this diversified generation might affect the end user. The example is of course greatly simplified but aims to describe a real phenomenon in the grid today.

2.3.1 Voltage drop

When moving down in voltage, the current must be increased in order to transmit the same amount of power. This leads to an increase of

thermal losses. Thermal losses causes a voltage drop over

the given transmission line. In areas with a weak grid these

losses can be of a non negligible magnitude and will result in

a lower voltage at the end user than at the substations low

voltage side. This is traditionally dealt with by upping the

voltage at the transformer to give the end user a good volt-

age[I].

(14)

Substation n

230V

240V 240V

250V

User Producer

Fig 4. Over voltage at end consumer when back-feeding the grid

Now we consider the case of the end user becoming a small scale producer of electricity. If he produces a larger amount of electricity than he consumes he will probably try to export the excess onto the grid. This means that he will have to overtake this voltage differential. Twice. This will effectively put him at 250V in the example illustrated. If the production originates from a stochastic energy source, such as solar photovoltaic, it would also give large instant fluctuations when quickly switch- ing between 250V and 230V.

This voltage drop can be seen in the grids of today, see fig 5.

Fig 5. Screenshot from the computer program “Power Grid” used by Fortum

(15)

2.3.2 Less traditional loads

The deviations from nominal power properties do not only depend on the feeding from the substation. They also heavily depend on the properties of the electrical load that the power is supposed to drive. The example above with voltage fluctua- tions is greatly simplified. For example, a grid with many electrical motors as loads has energy stored in the rotating mass of both the motor itself and its con- nected mechanical load. The grid therefore has an inertia counteracting the sudden voltage change described above. This phenomenon is a stabilizing factor in large interconnected grids and works better the higher the short circuit power is.

However, the continuing trend regarding the composition of electrical loads points toward a lower percentage of mechanical loads and motors and a higher percentage of micro and macro electronical loads[IV]. The mentioned regulating inertia, also known as frequency regulation, is therefore predicted to have a some- what smaller impact in the future. This suggests that an external support for grid stabilization might have to be considered.

2.3.3 Phase asymmetry

The ideal state of power is perfectly symmetrical three phase at nominal sinusoidal

voltage. But not all equipment we use run on three phase power. In practice, the

tradition has been to roughly divide the one phase loads between the phases. This

works quite well. However, in the case of small scale production one might not

consider the idea of three different inverter systems for one installation to be rea-

sonable. To add production in one phase would potentially cause symmetry prob-

lems.

(16)

Fig 6.Schematic view of different Power Quality phenomena

3 Power Quality

3.1 General and definition

The concept of power quality is not strictly defined. It varies with the requirements of the consumer and the electrical characteristics of the load of the consumer.

Therefore the responsibility of maintaining a good electrical environment falls upon both the distributor, the manufacturer of the application and the user of the application.

There are, however, several phenomena that can cause problems of different mag- nitude for a grid connected user. Examples of these are harmonics, voltage varia- tions, asymmetry between phases, frequency deviations and so on. All of these phenomena describe states that in some way deviate from the nominal state of the electrical characteristics, see fig 6.

- One can therefore define power quality as the absence of these phenom- ena.

Frequency variations

Distorted Phase Angle

(Active/Reactive power)

Voltage characteris- tics

Asymmetry Harmonics

Transients

Flicker Voltage

variations Power

Quality

Outage

(17)

3.2 A brief description of the phenomena [V]

3.2.1 Outage

Outage describes a state where the power supply is cut. This is defined as below 10% of nominal voltage. Outages are in many documents labelled “service reli- ability” and treated as a different kind of problem not really related to power qual- ity issues.

3.2.2 Frequency variations

Deviances from the nominal frequency which is in Sweden set to 50 Hz. Theo- retically, any node of an interconnected (AC) grid should have the exact same fre- quency. This is not the whole truth in reality. Weak parts of the grid have more local frequency issues in general than strong parts of the grid. Frequency devia- tions also tends to become an issue when dealing with islanding or closing in on such a state.

3.2.3 Phase angle

Refers to a situation where the voltage and current goes slightly out of phase to one another. This is created by the inductive part of the impedance of both trans- mission equipment and loads where motors and generators are significant con- tributors.

3.2.4 Transients

A temporary increase in voltage. Usually occurs when large units are connected or disconnected from the grid or by the act of thunder. A transient can increase the voltage by an order of magnitude lager than the nominal voltage. This does not however mean that they contain a large amount of energy as they are usually very short in time and low on current.

3.2.5 Harmonics

Signals of a frequency that is a multiple of the nominal frequency are called harmonics and are potentially very harmful.

3.2.6 Voltage variations

Called ”Swells” in the case of an increase and ”dips” in the case of a decrease.

Needs to be in effect over a couple of periods to qualify as swells rather than tran-

sients.

(18)

Fig 7. Citation of the Swedish law of electricity 3.2.7 Flicker

A quite subjective phenomena. The term “flicker” refers to the variations in light emitted by light bulbs. It is hard to define electrically and has a definition based on the perception of the human eye.

3.2.8 Asymmetry

The unbalance between the phases of a three phase system. An unbalance oc- curs when one or more of the phases displays a slightly different voltage, current or deviates from the 120 degrees phase shift supposed to be there.

3.3 Regulations and Guidelines Ellagen 3 kap §9:

” 9 § Den som har nätkoncession är skyldig att på skäliga villkor överföra el för annans räkning.

Överföringen av el skall vara av god kvalitet.

En nätkoncessionshavare är skyldig att avhjälpa brister hos överföringen i den utsträckning kostnaderna för att avhjälpa bristerna är rimliga i förhål- lande till de olägenheter för elanvändarna som är förknippade med bristerna.

Regeringen eller den myndighet som regeringen bestämmer får meddela föreskrifter om vilka krav som skall vara uppfyllda för att överföringen av el skall vara av god kvalitet. Lag (2005:1110).”

3.4 Official documents

Fig 7 is a quote from the Swedish legislation. It states that the transmission of power should be of good quality. Furthermore it states that the operator is obli- gated to remedy possible faults of the transmission to an extent that the benefit is reasonable in proportion to the cost[VII]. The legislation is in other words open to interpretation. The operator is legally obligated to measure amount of consumed electrical energy and its distribution over time for a connected consumer. There are however not any legal obligation to measure voltage quality[VI].

What is considered to be good power quality in Sweden is commonly agreed to be

in line with the guidelines provided in the European standard EN 50160; “Voltage

characteristics of electricity supplied by public distribution systems”. This stan-

(19)

dard provides threshold values for the supply voltage of a given grid. All of the phenomena in fig 6 are described there. It is however erroneous to only discuss the supply side of a given node. The electrical environment is also dependant of the dynamics of the load connected. Therefore, another series of standards have been developed called EN 61000 “Electromagnetic Compatibility (EMC)” with many subdocuments called EN 61000-1-2 etc. This series of standards specify how the connected equipment should behave electrically.

Together these sets of documents paint a picture of how the electrical envi- ronment should behave.

3.5 Crude guidelines

Many large installations require better power quality than the values allowed by the EN 50160[I]. Such installations may be process industry or something alike and are generally also large consumers. In those cases it is common for the pro- vider, consumer and manufacturer to through a discussion reach a level of quality that is most beneficial. This is the most cost effective way to deal with power qual- ity issues but puts high demands on the competence of the consumer in order to be feasible.

3.6 Actual threshold values

A good overview of the document EN 50160 can be found in an interpretational

document called “voltage disturbances”[VIII]. Here we also see the comparison to

the EN 61000 document sets which gives a better perspective on the regulations

for electrical environment.

(20)

Fig 8.Table of threshold values of EN 50160 and EN 61000 [VIII]

(21)

3.7 Comments to EN 50160

It is important to keep in mind that the strife for good power quality should not be a goal in itself. Many (or actually most) applications do not require perfect power quality and it is therefore unreasonable and uneconomical to create an environ- ment with perfect power quality. The stakeholders should instead, through a dis- cussion, settle on a level that is most beneficial for all parts. Industries and com- mercial consumers also in general require a higher level of power quality.

The EN 50160 is under revision. A European cooperation is undergoing to re- vise this standard and a set of recommendations have been presented by ERGEG and is supposed to be accepted as changes to the existing version[VII].

The above mentioned EN 50160 set to describe the properties of the supply vol-

tage is limited to only apply under normal operating conditions. This of course

means that when an event occurs, planned or unforeseen, the grid is immediately

outside of normal operating conditions and a customer cannot claim the protection

of EN 50160.

(22)

4 Dangers and implications of bad power quality

To further motivate the conduction of this study some words regarding the conse- quences of bad power quality should be mentioned.

4.1 Fortums distributing role

Fortum is because of their position as electricity provider responsible for the prod- uct they deliver, namely electricity. Therefore they occasionally get damage claims from customers who have in some way received a bad product. Since the legislation in Sweden is open to interpretation[VI] and measurements at a single user are very seldom carried out, a big lack of information is common in such cases. A section within Fortum that works with damage claims handles the re- ceived claims and cross check the time of the reported incident with records of non ordinary behaviour in that region of the grid. This can be due to repairs, malfunc- tions of equipment or new installations in the area. But over all the information is scarce, especially specific details about exactly what has electrically happened at the feeding point of an end consumer.

4.2 Protection

The low voltage grid is protected only by breakers that react to large currents and short circuits. There is traditionally no protection against voltage variations[IX].

This is due to the fact that the voltage is relatively stable which means that high currents represent high powers. High powers are what is dangerous to persons and property. This is regulated by elsäkerthetsverket in Sweden and follows more strictly defined regulations than power quality since it is considered a safety issue.

The simple principal of this is that the series of interconnected conductors that

constitutes the grid always are dimensioned for a maximum power flow. A breaker

is installed as the weakest link of a section of conductors and will hence trip and

cut power at a set value of current flow to protect the installation. This principal is

(23)

used in all voltage levels of the grid and manifests itself at the end consumer as a fuse.

4.3 Common customer damage claims

Many of the problems reported to Fortums damage claim coincide with faults on the zero conductor. Modern installations in buildings include a residual-current device (jordfelsbrytare), required by law on public buildings and outdoor installa- tions. The design of the residual-current device is made to cut power when a dif- ference between phase current and PEN current is detected, i.e. current leakage.

Older installations are not protected in this way and are susceptible to zero con- ductor faults. Such a fault often occurs together with maintenance or repair work.

Such a fault can potentially give 1 phase equipment a voltage of 400V instead of the nominal 230V[IV]. This often leads to extensive equipment damage but can also be a safety hazard.

Fig 9. Left: PEN conductor lost. Right: short circuit between a line and neu- tral[IV].

Claims can then typically include domestic equipment such as dishwashers, refrig-

erators etc. In some cases, claims can include virtually all electrical equipment in

the house [X]. A received damage claim is treated by Fortums personnel who open

a case for investigation. The case is then revised and the incident is cross checked

versus known incidents in the grid matching the time interval given such as main-

tenance work or detected faults. If the claim is for a larger amount of money, in-

surance companies usually handles the process of juridical responsibilities. For-

tums investigators also do this for claims of lesser values. The previously men-

tioned lack of information is however a big issue. In cases where there are no in-

ternal records of deviances from normal operation it is a case-to-case decision.

(24)

Since all decisions needs to be backed up by documentation, installation electri- cians and entrepreneurs are consulted for a professional statement. In cases where there is no relevant data to consult a decision is made on a probability estimation.

4.4 A theoretical example

Problems may arise when consumers connect large temporary loads, especially if they are one phase connected. A good example can be a part of a suburban grid with a few villas connected to the same substation where the grid is not too strong.

If one of the consumers connects a welding machine running on one phase power it will probably affect his neighbours in a negative way. Such a load is an intense power consumer and is also rapidly switched on and off. Visual effects will be flicker in lights connected to the same phase and possibly a brief hiccup in electri- cal motors such as fans. Unnoticed effects might be three phase connected motors damages such as washing machines, dryers, water pumps etc. who receive an un- balanced power input. This will be extra bad if the electrical characteristics of the load contain a big inductive part, in which case three phase motors will be sub- jected to a counteracting magnetic field which will lower its efficiency and cause more wear and tare. Such a scenario is clearly caused by the introduction of an exceptional load but the responsibilities are not clearly defined, see section Power Quality. The welding machine should obey the emission standard SS-EN 61000-3- 2 [XI]but even if it does so the neighbours might experience problems in a weak grid. This results is a situation where the electricity provider has kept up his end, the welder producer has kept up his end but some customers still experience a de- generation of their power supply. This knowledge of the behaviour of the low voltage grid is far from general knowledge among house owners. From a custom- ers point of view the product they are buying is suddenly changing from good to bad without them changing anything. A survey carried out by Elforsk shows that customers put responsibility foremost on the electricity provider, secondly on the electrical installation entrepreneur. The device manufacturer comes in third place and on fourth neighbouring consumers[XII].

4.5 Costs related to power quality on a national scale

Elforsk has in December of 2006 put together an evaluating report about power

quality and its implications[I]. This report evaluates the full national electrical sys-

tem from small apartment consumer to major processing industries, but it still

helps us to put economical figures on the issue of power quality in the low voltage

grid. A good overview table can be found on page 44

(25)

Fig 10. x-axis reads “process industry, production industry, commerce, office, real estate, public, rural, households”, y-axis reads “long outages, short outages, tran- sients, voltage variations, harmonics, voltage asymmetry, flicker” . Digits are in million SEK. “begr” means “limited”[I]

4.6 Discussion about power quality costs

Dissecting this table we can see that outages in general are by far the most expen- sive power quality problem. This is also the most well-documented phenomena.

The cost is mainly due to production interruptions. The high figures for short out- ages is because a short interruption or power dip often trips safety equipment and takes some time to restore. In this way, a power cut of half a second can result in production interruption of several hours. This is obviously not desired and many large power consumers have supporting equipment of their own to guard them- selves against this.

When looking at domestic households, transients and voltage variations stand out

as big expenses. This is interesting for the topic of this thesis. The figures pre-

sented correspond almost exclusively to damaged equipment. A big part of this is

equipment connected to two or more electrically signalling grids, e.g. distributing

network and tele network. An over voltage in one of them gives an unnatural volt-

age difference between the two systems. This difference will be present inside of

(26)

the device which the device is generally not constructed for. More on this in sec- tion “Detailed description”. Even though these estimations are quite rough they still provide some idea of what good power quality at the end consumer could be worth. This of course has to be weighed against the investment needed to re- duce/eliminate the given problem.

Another report from Statens Energimyndighet dated 2003[XIII] states:

Fire in property due to over voltages:

xa100 x 1 million

100 Damages to domestic and office electronic devices etc covered by

home- and property- insurances:

22 000 x 10 000 kr

220

Damages covered by product warranty: 50

Damages to electronic devices not covered by insurance: 150

Sum 520

As we can see, Fortum does not carry the heavy financial burden of bad power quality. The Cost is distributed among all the actors. This can be considered rea- sonable given the previous discussion about the shared responsibility regarding the electrical environment. All documents regarding power quality stress the fact that a reasonable electric environment must be achieved through cooperation between the parts involved. But when looking at the financial part of the problem, an addi- tional actor enters the scene. Insurance companies. There are examples of cases when legal processes are carried out between Fortum and insurance companies regarding financial compensation to a customer. This can be a hot subject if for example a full out fire has occurred in a real estate worth very much money. If the fire is severe, the evidence is probably damaged and a lengthy legal process may be the result.

4.7 Good power quality is sought

As a final word to conclude it can be said that that a good electrical environment, good power quality, is worth a significant amount of money for all parts involved.

The price for bad power quality is divided among the stakeholders with an over-

weight on the consumer and commercial players. The price to achieve good power

quality, the investments needed to be made, is also divided among the players[I].

(27)
(28)

5 Solar cells

5.1 History

Electricity production from solar cells is also called PhotoVoltaic generation. The phenomenon was first discovered by Alexandre-Edmond Becquerel (father of Henry B.) in 1839 . This is about the time when humanity first started to discover electricity (Faraday’s law of induction in 1831) and the vast possibilities of elec- trical energy was not yet known. The first selenium solid-state cell was invented in 1876. The next big leap comes with the introduction of semi conductors in the 1950:ies. The modern silicon solar cell was invented at Bell Labs in 1954. It found a natural niche in the space program and the first silicon solar cell was launched in 1958. Power generated from sunlight and without moving parts is of course ideal for this purpose. This helped the development greatly because of the abundant fi- nancial funding of the likes of NASA[XIV].

5.2 Functionality

A solar cell is essentially a diode. It utilizes the photoelectric effect which means that electrons are energized by photons; light. In a semi conducting material such as silicon, with four out of eight possible electrons in its outer shell, this means that an excess electron is knocked loose to move freely in the crystal structure. As the electron is knocked loose, a gap appears where it was located. This gap also moves freely and is labelled a “hole” and treated as a particle of its own. The pho- ton has thus created an electron-hole pair.

The natural thing for the electron and the hole to do is to quite soon find each

other and free the energy now bound in them into dissipating heat. To prevent this,

the silicon is doped. Doping means that some impurities are introduced in the crys-

talline structure. Materials introduced include one extra, or one less, electron in its

outer shell. This shortage / excess of electrons create an electric field between

(29)

Fig 11.Schematic view of a Solar Cell

them. This electric field separates the electrons from the holes which are attracted to opposite sides of the cell. When the two sides are connected by an external con- ductor a current arises. The solar cell is complete see fig 11.

5.3 Electrical characteristics

A single solar cell is, as shown in figure above, has only one voltage level. In a silicon cell it is 0.6-0.7 V. This is a quantum mechanical property of the semicon- ducting element silicon. The distinct value corresponds to the potential difference between the valence band and the conducting band within the silicon and corre- sponds to any photon carrying an energy of 1.2 eV or higher. This means light of wavelength 1022 nm or shorter 1 . An increase of the area of this theoretical cell will increase the irradiance of light fallen upon it which will increase the number of electron-hole pairs created. This will increase the current that can be drawn from the cell but will not affect the voltage.

Since a voltage level of 0.6 V is very low something must be done to up the level. This is done by connecting several cells in series into modules. Theoretically this principle can be used to reach any voltage level desired. But the trade off in doing so is that the module, being a closed electrical circuit will have its current limited by its least conducting cell, the “weakest link of the chain”. This practi- cally means that if an obstacle located as illustrated in cell “B” in fig 12 below will

1

E = h * f → E = h * c / λ → λ = h * c / E = 4.13 * 10

-15

[eVs]* 2.97 * 10

8

[m/s ]/ 1.2 [eV]= 1022

* 10

-9

[m]

(30)

Fig 12. Solar cells and batteries connected in series

limit the array to about 95% of its capacity, whereas an obstacle as illustrated in cell “C” in fig 12 will make the whole array dead[XIV].

The electricity production of solar cells is also temperature dependant. The hotter

the cells get, the lower efficiency they get. Efficiency is also limited by obstacles

(as illustrated above), malfunctioning or inferior cells and of course whether the

sunlight is direct or indirect. Fig 13 below shows a theoretical solar cell’s electri-

cal variances.

(31)

Fig 13. I-V curve of a solar cell [XIV]

In figure 11 X-axis shows voltage, Y-axis shows current. The green curve illus- trates a cells ability to conduct current without being hit by sunlight. This curve resembles the conducting curve of a diode. The blue curve, which is almost identi- cal to the green curve except a constant is added, shows a solar cells ability to conduct (create) current when illuminated by light. The point marked “I SC ” on the Y-axis is a theoretical maximum current the cell can create when short circuited.

Similarly the point marked “V SC ” on the X-axis is the voltage across the cell when

no closed circuit is made and the voltage is measured across the cell. This voltage

should in the ideal case be the previously mentioned 0.7V but is in reality closer to

0.5V. Depending on I SC , V SC and the shape of the blue curve, the red curve is de-

rived. The red curve stands for output power, I * V, and is of course what we are

looking for in electricity production. As shown in picture there is an optimal rela-

tion between current and voltage at which we want to operate in order to reach

maximum efficiency. This is achieved by controlling the load in the circuitry to

draw the exact amount of current that corresponds to the cell’s, or rather the array

of cells’, “I MP ”.

(32)

5.4 Output of power

The load in this case is a power inverter. An inverter takes DC power as input and inverts it to AC power, in this case 230V 50Hz to feed the grid. In order to be able to feed the grid, and not have power fed from the grid to the inverter, the in- verter needs to keep a slightly higher voltage than the grid has at the point of con- nection. In the same way the DC input voltage from the solar modules must be slightly higher than the input at the inverter. (For the same reasons a similar con- trol system is also required when charging batteries from solar cells even though both batteries and solar cells operate on DC power.) This obviously introduces the need for a dynamic control system in order to be kept working at a good effi- ciency. It is usually this full control system and its power electronics that is called inverter.

From the grids point of view there is just an inverter. The electricity is “created”

in the inverter and one can therefore make the argument that it is an electrically robust installation. Disturbances and deviations (however unlikely) in the main producing PV-arrays would not carry through to the AC power output.

The inverter furthermore inverts the power created by the installation. If less

power is created the inverter stays with the same voltage level but lowers its power

output. Therefore the system will affect the grid the most when the power output is

the highest. Thus, the thesis is focused on the installations maximum rated power.

(33)

6 Other components in Stockholm Royal Seaport

6.1 General

The previous chapter about solar cells was chosen because it is the main new component close to the end user. It was also chosen because it serves as a good example of other components. Since the objective of the thesis was to look into possible power quality issues at the end consumer, it does not exclusively concern solar power. However, there is a lot to be learned by studying the properties of solar power.

6.2 PV generation and batteries

The power electronics controlling the cells and making proper power output from them are the key. These power electronics are very much the alike the con- trolling electronics for batteries. They have an energy source operating in a certain voltage interval. For solar cells the voltage varies within the interval with obsta- cles, temperature and other minor aspects. For a battery it varies with the charge percentage, age, temperature and so forth. The electricity sources are in other words very similar. The inverter then takes this as input, keeps it at optimum volt- age level and transforms the power to nominal grid AC. (A big difference obvi- ously being that the electronics for the batteries needs to be able to charge the bat- teries as well as draw power from them.)

The figure below shows the schematic outline of the “passive house” and its properties thought to be implemented in Stockholm Royal Seaport. Worth noting is that 100m 2 of solar cells corresponds to roughly 14kW power (peak effect) which is strikingly close to the 13kW suggested for the batteries[II].

The yellow square with a blue lid in the apartments represent controllable loads

that the smart grid operator can use to balance power consumption over time.

(34)

Fig 14. Schematic view of the “active house” of Stockholm Royal Seaport

6.3 Electric cars

The electric cars are thought to be a key component in grid management. They are thought to be charged at night to balance power consumption over the 24 hours of the day. But electric cars are still a few years into the future and have therefore not been a main focus in this thesis.

• 1 Building

• 40 apartments

• Normalized consumption pro- file according to research in Elforsk report 8:54,

• Estimated consumption of 4100 kWh per house- hold/year

• Controllable loads dishwash- er and textile washing/dryer, Total 43 kWh/daily

• Photovoltaic generation, 10 000 kWh/year (100m2), 48kWh 200 days/year

• Battery size 13 kW, 54 kWh

recycled daily, approx 1500

kg batteries

(35)
(36)

Fig 15.Schematic view of different Power Quality phenomena

7 Detailed descriptions of PQ phenomena and its effects

7.1 Outage

Outage is the most dominant part of quality issues and also the easiest to measure and find data records of. Outages are always caused by a fault, either spontaneous or as a result of human error. An outage is comparably easy to cost-estimate. An outage effects industry the hardest, especially production industry where a lack of production of course leads to significant costs[I].

The costs for a domestic user are harder to estimate. There are of course examples though. A case from damage claims tells a story where an outage to a summer cabin in Dalarna caused the pipes to freeze and Fortum paid damages for 37000SEK[X]

An outage of more than 12 hours is compensated economically with a minimum of 900SEK and a maximum of 300% of the customers’ estimated yearly feeFel! Hittar inte referenskälla.. Outages of this magnitude are generally rare and very rare in urban areas.

Frequency variations

Distorted Phase Angle

(Active/Reactive power)

Voltage characteris- tics

Asymmetry Harmonics

Transients

Flicker Voltage

variations Power

Quality

Outage

(37)

It is harder to estimate the cost of short outages, but these are on the other hand easier to visualize. The time loss of equipment not functioning when needed (stove, washing machine etc) and the scenario of work lost on the computer. Most often a blackout is not depending on bad feeding from the grid but from safety tripping within the house or property.

7.1.1 Outages in Stockholm Royal Seaport

The introduction of new electrical components poses a somewhat enlarged risk for outages due to the lack of experience. However, ABB who provides the control system for the smart grid has expressed the reliability of the grid to be a priority. It is therefore the authors’ opinion that there will not be an enlarged risk of outages within the test area Stockholm Royal Seaport.

7.2 Frequency variations

The frequency in the Swedish grid is set to 50Hz. This means that all synchronous machinery electrically connected to the grid operates at this frequency. A variation in this frequency is the grids natural response to a change in production or consumption in the over all national balance of power. If a big production unit, e.g. a major hydro power plant or a nuclear reactor, the frequency will drop a little. If on the other hand a big power consumer falls off the grid the frequency is slightly increased. This is managed on a national level by Svenska Kraftnät who are put in charge of balancing production and consumption at all times.

Many direct connected motors and generators give the grid a certain mechanical inertia. A way to visualize this is to imagine a big rotating motor rotating at a speed corresponding to 50Hz. If there is a sudden lapse in production, the rotating mass of the motor will in accordance to all physical theory want to keep spinning at the same speed and will therefore make the sudden change more smooth.

Deviations in frequency affect clocks that use the electrical frequency of the grid to know what time it is. Such clocks are common. Robotics with direct driven motors would also go out of sync if fed with bad frequency.

In weak parts of the grid frequency variations are uncommon but possible. When

approaching islanding operational mode frequency deviations are more likely. If

absolutely zero power is exchanged in a node connecting a self sustaining grid part

and the overlaying grid it is theoretically possible for that part to have a frequency of

its own.

(38)

7.2.1 Frequency deviations in Stockholm Royal Seaport

Although island state could be considered due to the local production in SRS, the generation is of such low magnitude that no problems are expected. Studies have shown that a ratio of 70% local production nominal power of the feeding transformers power is quite manageable by the grid. Also, as mentioned above, the local power produced would be manufactured on site with near perfect properties.

7.3 Phase angle

The concept of a phase angle is a mathematical way to deal with a slight time lag between voltage and current. The word “phase” in this section does not correspond to a “phase” used in the below description of three “phase” systems but simply represents the previously mentioned time lag, voltage and current are “out of phase”. Phase angle directly correspond to the concept of active and reactive power in the way that cosine of the phase angle equals the fraction of the apparent power that is active. Analogy, sine of the phase angle gives the fraction of reactive power.

Reactive power is something useful for some applications, especially induction motors require some reactive power to magnetize their rotor. When transporting electricity, reactive power leads to losses and is therefore something that one wants to avoid. Reactive power is dealt with by capacitor banks installed at key points in the grid. Industrial power users sometimes create reactive power of which they are charged with a fee by the distributing company. Many large power consumers there- fore have their own phase compensation.

7.3.1 Phase angle in Stockholm Royal Seaport

Given the characteristics of the solar cell invertors, who creates power with a power factor of 1 (no reactive power), it is considered unlikely that Stockholm Royal Seaport will have a larger risk of reactive power problems than any regular part of the grid.

There is also not to the authors knowledge any electrical device with a particular large inductive part considered to be introduced.

7.4 Transient over voltages

Voltage transients are in many ways interconnected with voltage variations. The

definition of a voltage transient according to EN 50160 is a “brief oscillating or non-

oscillating over voltage, usually heavily dampened with a duration of a few millisec-

(39)

onds or less”[V]. Transients are caused by lightning or switching operations, for example when a high inductive current is switched off [VIII]. The standard does in this case express itself a bit unclear. It states “transient over voltages does normally not exceed 6kV peak value, but can occasionally reach higher levels”. It does not actually give a recommendation that transient voltages should not exceed this value, or any other.

While 6kV seems like an extremely high voltage level compared to the nominal voltage of 230V its effects are not as dire as expected from such a deviance. Given the time span of maximum 5 milliseconds and down to microsecond level they do not carry much energy[V]. A period is 20 milliseconds in a 50Hz AC power system.

These high frequency and low energy transients constitute the kind of transients that presents lesser danger. Transients of low frequency and higher energy present more of a problem. They can slip though protections because of their lesser height of the spike.

This is in reality an energy pulse carried by the grid. Voltage transients are in many ways connected to current transients; see section below under “voltage variations”.

Voltage transients are dangerous in equipment connected to two or more electrical signalling networks. Phones, faxes, computers and TV’s are all connected to the power grid but also to either data network, tele network or TV network. If one of these networks are carrying a transient into a device there will be a potential difference within the device between the two signalling networks and a flashover, a discharge, will probably occur which is harmful to the device [XIII].

7.4.1 Transients in Stockholm Royal Seaport

To control the smart grid in Stockholm Royal Seaport a signalling system called SCADA (Supervisory Control And Data Acquisition) is planned to be installed. It is not yet decided whether this will be a physical network or information will be sent via the wireless GSM network. A physical network parallel to the power grid will pose an increased risk of transient damages to the SCADA system. This risk increase is however considered marginal by the author. For one, there traditionally are very few transient problems in urban areas especially in urban areas newly constructed. The high short circuit power of the grid also works to an advantage to decrease voltage transients. Current transients may however pose a problem, see section “voltage variations” below. A second reason is the previous experience from SCADA systems.

7.5 Harmonics

Harmonics have historically been considered a lesser problem in Sweden than in the

rest of Europe. This is because Sweden has been a heavy power consumer per capita

with electric heating. Electric heating is electrically a very nice linear load and a

system built up of many of those helps to smooth out and reduce harmonics. As we

(40)

move forward into the future with more environmental awareness and a changing energy system striving for more efficient power use we gradually try to eliminate this use of electricity, and hence approach the continental situation[I].

Harmonics are voltage or current components of a multiple of the grid base fre- quency 50Hz. They are created almost exclusively at the consumer. With no regulating equipment they travel upwards and spread in the grid. Harmonics are created by non linear loads that draw a current of another plotted shape than the one of the voltage.

Depending on the strength of the grid, the impedance, the non linear current affects the voltage and distorts the sine shape of the voltage too.

Harmonics are harmful to equipment and causes heat losses. They also have an unwanted effect to occasionally create resonances between inductive and capacitive parts in the grid which leads to non useful power transportation which means unneces- sary losses. The 3:rd over tone is especially harmful since it adds itself up in the PEN- conductor which can then lead to vagabond currents. Another aspect which is hard to estimate economically is pulsating torque effect that occurs in motors fed with power tainted by overtones. Equipment using clocks that are based on the grids 50Hz fre- quency can also experience problems from harmonics with amplitude big enough to create false intermediate crossing of zero potential. Harmonics are generally dealt with by filters. This erases or restrains the harmonics by dissipating it as heat, which are obviously losses.

7.5.1 Harmonics in Stockholm Royal Seaport

It is estimated that 70% of all global electrical power pass through rectifiers[I]. All rectifiers are non linear loads. Rectifiers using PWM-switching are becoming more common and use a very high switching frequency. Generally a higher switching frequency creates less harmonics but there is a risk for the high order switching to interact with other equipment of the same type. Resonance between two or more components can in its own create harmonics. Different switching apparatuses can also counteract each other. The author would suggest some thought would be given to this matter in selection of apparatuses.

7.6 Voltage variations

Voltage variations are, together with frequency variations, the grids natural reaction

to a change in load or production. Voltage increases are called “swells” and decreases

are called “dips. As stated in the section “Power Quality” we are approaching an

environment with less grid inertia as the fraction of electronic loads compared to

electric machinery is increased.

(41)

7.6.1 Swells

Swells are in general dangerous to equipment[IV]. A device constructed for 230V will in most cases function normally on 240V but is not healthy in over long stretches of time.

In high voltage parts of the grid some protections against over voltage is installed. It is simply put a device between two conductors that short circuit them[I]. This device, called over voltage protector, starts conducting at a certain threshold value but is an isolator at nominal voltage. In low voltage parts of the grid there are no such protec- tions since the cost does not motivate the benefit [IV].

Swells are related to transients. The difference is one of definition, a transient is very short whereas a swell endures several seconds or is permanent. Swells are uncommon.

7.6.2 Dips

Dips are however more common. On a national average there occur about 20 dips every year in Sweden[IV]. Dips are indeed the sign that the protection systems within the grid are functioning properly. Dips are caused by switching operations in the grid, operations mostly caused by faults such as short circuits or PEN-faults. This can be because of thunder, trees or man-made breaks on cables and the following disconnects and circumventions of the fault.

A report by Elforsk suggests that dips are especially dangerous to electronic equip- ment[IV]. A, at the time of its publishing, still not practically proven theory is intro- duced that suggests dips as the indirect reason of several malfunctions on electronical devices.

7.6.3 Current transients

Large over currents on a large scale are limited in the grid. This is because protec- tions are installed to cut faulty parts or components of the grid if they draw an unnatu- rally large current. Since the voltage pretty much keeps steady it is the current drawn that determines the power delivered/used. Therefore safety breakers are installed mainly in the substation but also in different nodes in the grid and this eliminates the danger of excessively large transient currents.

It does not however cover small fluctuations and current surges. For this we obvi- ously have a personal safety legislation that guides how to safeguard a home with domestic breakers. But they still might allow a current transient high enough to damage electrical equipment.

Elforsk did in 2006 write a report investigating the sensitivity of electrical equip-

ment with the main focus on equipment connected to two different signal networks,

e.g. power grid and tele grid. The investigation shows that current transients can occur

very locally and damage or destroy electrical equipment which is not sufficiently

(42)

protected . An identified weakness is that the conventional rectifier contains a protec- tion for cold starts, but not for sudden current rushes following a voltage dip in the grid. When a local or more spread out voltage dip occurs in the grid due to a start-up of a significant additional load or similar, the grid quickly strives to balance it and return to nominal voltage. During the dip, capacitors in the conventional rectifier have emptied out its energy and now receive a sudden current rush which damages the equipment.

Generally, equipment is protected against cold starts to limit inrush currents. These protectors are however set out of play in the case of temporary dips[IV].

7.6.4 Voltage variations in Stockholm Royal Seaport

Dips are less common in urban areas than in rural areas, mean value of 0.8 per month compared to 3.5. The phenomenon in its own however becomes more danger- ous because of the high short circuit power in urban grids. A high short circuit power, low grid impedance, makes current rushes larger and more instant. Since dips are mainly caused by switching operations in the grid and a smart grid such as the one considered for Stockholm Royal Seaport will probably have more switching opera- tions per given time unit than an ordinary grid this phenomenon might have to be given some consideration. There is technical protection equipment that can be installed to circumvent this. The author does not however believe that there will in practical reality be a real problem with voltage fluctuations. A part of this is that the battery buffer will help keep the grid stable at end customer.

7.7 Flicker

Flicker is a very visual type of power quality problem. It originates from fast volt- age fluctuations and makes a visual impact in light bulbs. The definition of “flicker” is not electrical, but constitutes of a subjective perception of the human eye. It is still measured by a device and has two types of values; Pst and Plt (short- respectively long- term severity). Flicker is typically created by electrical emmittance from facto- ries using arc cutting elctrodes in the high voltage region. In low voltage grids emit- tance sources can be welding machines, elevators, heat pumps etc. The grid impedance is a big factor here.

Flicker is mostly unpleasant to the human eye/brain but does not constitute much of

a danger to equipment. In fact, the voltage fluctuations causing the flicker is usually

very much within the margins of what is considered good voltage levels. It is treated

as a power quality issue of its own due to its resonance with what the human eye is

(43)

sensitive to. It is easily reduced by the use of low energy light bulbs instead of regular light bulbs[XVI].

7.7.1 Flicker in Stockholm Royal Seaport

Flicker is a phenomenon generally occurring in weak grids. The grid planned for Stockholm Royal Seaport will be designed to be strong and somewhat over dimen- sioned to meet possible future demands. It is therefore the authors opinion that flicker levels will not be a problem in Stockholm Royal Seaport.

7.8 Asymmetry

In the three phase system we have today we say that the system is balanced when the phases are equal in magnitude, sine-shape and lags exactly 120 degrees (or 1/3 period) after each other. An unbalanced system is called asymmetrical. Virtually all tools of calculation used by electrical engineer today are based on a balanced system.

Calculations on asymmetrical systems quickly become very complex and very soon become incomprehencible. As a tool of to be able to calculate related problems, a system of symmetrical components is introduced. It is an estimate of an unbalanced system that consists of a zero, positive and negative sequence components . Unbalance is measured as the ratio between positive and negative sequence components ex- pressed in percentage.

An unbalance larger than 1% is uncommon. EN 50160 allows 2% for 95% of a weeks measurement but leaves room for an occasional 3% at certain points[V].

Unbalance in the high voltage transmission grid is caused by unsymmetrical loads which mean that the conductors for the three phases for some reason have slightly different impedance. Unbalance is more common in the low voltage grid where local values of 2% may occur[XVI]. The unbalance here is mostly due to non evenly distributed one phase loads.

Unbalanced power affects three phase motors and transformers and leads to excess

heat losses. This is because two different magnetic fields create resisting torques, one

rotating and one stationary. This causes induction heating of the motor and makes the

motor run on a lower efficiency than normal with excessive heat development as a side

effect. A result of this is a shorter life of the motor as well as more expensive opera-

tion . Frequency rectifiers are more sensitive. Frequency rectifiers are used to drive

motors of a different frequency than the nominal 50Hz and are mostly used in indus-

tries. Even at an unbalance of 1.5% the equipment may trip because it at that point

(44)

Fig 16. Evaluated view of different Power Quality phenomena

only draws power from the two strong phases which makes breakers react to an abnormal current consumption[XVI].

7.8.1 Asymmetry in Stockholm Royal Seaport

Even though we are moving in a direction of traditional three phase loads becoming one phase loads it is not suspected that there will be a higher unbalance in Stockholm Royal Seaport compared to traditional domestic areas. This is also based on the assumption that the solar power installed will generate three phase power which seems to be a reasonable assumption.

7.9 Summary

Areas marked yellow symbolize areas that may require extra attention in the realiza- tion of Stockholm Royal Seaport due to reasons stated above. Green areas are areas that in the authors opinion does not require special attendance for this particular project compared to ordinary new constructions.

This is all evaluated from the end customer’s point of view, at the very end of the vast national electric distribution grid.

Frequency variations

Distorted Phase Angle

(Active/Reactive power)

Voltage characteris- tics

Asymmetry Harmonics

Transients

Flicker Voltage

variations Power

Quality

Outage

(45)

References

Related documents

The dis- crepancy with IAS 1, Presentation of Financial Statements applied when designing the consolidated accounts primarily relate to the reporting of financial income and

För säkring av osäkerheten i framtida ränteflöden avseende lån till rörlig ränta används ränteswappar. Ränteswapparna värderas till verkligt värde i balansräkningen.

However, to successfully teach culture, media literacy and intercultural competence through film, preparational as well as follow-up work are essential and the

So I’m assuming we now have an agreement to sell you a car.” One agency I trained with taught us to test the assumed closed by stating/asking (auto salespeople are good at

The first design to switch the power to the ignition coil on and off in order for the spark plug to spark, was based on a computer programmable micro controller board sold under

Sampling the system (or, equivalently, generating a system sample) means to randomly assign a value, within the set of the possible values and according to the

– Event-driven designs using asynchronous circuits – Dynamic power management for controller design – Construction of VLCs and their CODECs.. – Circuit design for

Important variations (cf. Important events are rapid voltage changes, dips, swells and interruptions. the disturbance levels) results from the interaction between the