Control and synchronization of a marine substation

UPTEC ES09 026

Examensarbete 20 p Oktober 2009

Control and synchronization of a marine substation

Boel Ekergård

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

Control and synchronization of a marine substation

Boel Ekergård

Wave energy is a renewable energy source with great potential. Series of different techniques have been developed to achieve a power plant that can convert the kinetic energy in the waves to electrical energy. One of these concepts has been developed at Uppsala University. The converter is a linear direct driven permanent magnet generator, placed on the seabed, driven by a buoy on the ocean surface.

The output voltage from the linear generator varies both in amplitude and frequency.

To be able to feed the output voltage to the grid, the voltage is converted to suitable properties and synchronized with the grid voltage. Different methods to achieve the synchronization have been investigated. Simulations in the software program Simulink and LabVIEW FPGA have been performed.

The substation includes a tap-transformer with five different taps on the primary side.

Different systems to achieve a safely on load tap change were investigated. The results from the investigations are based on simulations in Simulink, LabVIEW FPGA and calculations, and are well consistent with the theory.

ISSN: 1650-8300, UPTEC ES09 026 Examinator: Ulla Tengblad

Ämnesgranskare: Mats Leijon Handledare: Cecilia Boström

1

Svensk sammanfattning

Världens energisystem är idag beroende av fossila bränslen. Mellan 70 och 80 procent av världens energi kommer från olja eller kol. Genom förbränning av olja och kol frigörs energi som kan konverteras till elektrisk och kinetisk energi. Vid förbränningsprocessen bildas växthusgasen koldioxid, CO2. Mängden koldioxid i jorden atmosfär har på grund utav detta energisystem ökat. Hur detta kommer att påverka vår natur är en fråga med många olika svar, men starka bevis pekar på en ökad temperatur med ett mer extremt klimat med starkare och kraftigare stormar. Den ökande temperaturen leder till att ökenområden breder ut sig och till smältande glaciärer och polarisar som leder till ökad havsnivå. Detta är ett problem som inte kan bortses ifrån och en stor anledning till varför utvecklingen av förnybar elproduktion är viktig.

En energikälla som inte har använts storskaligt är rörelseenergin i vågor. Utmaningen att konstruera en energikonverterare som klarar av havets ogästvänliga miljö är stor, men många olika sorters tekniker har tagits fram.

På avdelningen för elektricitetslära vid Uppsala universitet har en av dessa tekniker utvecklats. Designen består av en boj kopplad till en direktdriven permanentmagnetiserad linjär generator placerad på havsbotten. Bojen är kopplad till generatorns enda rörliga del, translatorn. När bojen hävs upp och ner av vågorna följer translatorn med och den önskade relativa rörelsen mellan generatorns translator och stator har uppnåtts. Valet att arbeta med en direktdriven generator är gjort för att kunna eliminera många mekaniska delar, till exempel växellådor. Genom detta val kan en robust och hållbar konstruktion erhållas.

Spänningen ut från en direktdriven permanentmagnetiserad generator varierar både i frekvens och amplitud. Skall denna spänning kunna kopplas in på det nationella nätet, måste den konverteras. Ett marint ställverk har på grund av detta adderats till systemet, mellan generatorerna och nätet.

Det marina ställverkets huvuduppgift, ihopkopplingen av effekterna från de olika generatorerna har kompletterats med konvertering av generatorernas utspänning till nätets egenskaper. För att detta mål skall uppfyllas likriktas spänningen genom en likriktare. Den amplitud varierade likspänningen laddar upp en kondensatorbank, varvid en stabil likspännig ut från banken kan uppnås. En växelriktare konverterar likspänningen till en växelspänning med önskad frekvens. Växelriktaren är uppbyggd av aktiva elektriska komponenter, så kallade IGBT:er. Dessa aktiva komponenter behöver styrning. Ett kontrollsystem till växelriktaren behöver konstrueras. Detta kontrollsystem skall även kunna synkronisera växelriktaren med nätet och se till att växelriktaren följer nätets frekvens. Det sista steget i ställverket är en upp- transformering av spänningen och genom filtrering reducera halten övertoner.

Vid olika vågklimat nås troligen maximal levererad uteffekt från generatorerna vid olika elektriska dämpningar. För att kunna undersöka detta är transformatorn i ställverket en så kallad tapptransformator. Den använda tapptransformatorn har fem olika tappar, det vill säga ingångar, på primärsidan, varvid fem olika primärspänningar kan fås. Genom att byta aktiv tapp fås en ny spänningsnivå och en ny nivå på den elektriska dämpningen har erhållits.

Ett mål med detta examensarbete har varit att konstruera ett system så att ett tappbyte kan göras smidigt utan effektavbrott. Jag har undersökt kommersiella system och även utvecklat ett helt unikt koncept. De olika systemen har testats i simuleringsprogram och deras för- och

2 nackdelar har vägts relativt varandra, där säkerhet har haft den tyngsta rollen. Resultat från simuleringar och beräkningar för de olika systemen har jämförts, och ett alternativ har tagits fram som förslag till slutversionen.

Den andra delen av detta examensarbete har varit att utveckla kontrollsystemet till växelriktaren. Utvecklingen skulle omfatta möjligheten för växelriktaren att synkroniseras mot elnätet och följa nätets varierande frekvens. Jag har utvecklat olika algoritmer för att uppnå detta mål och genom lärdom om mjukvaruprogram och hårdvarusystem har de testats.

Lyckade experiment har utförts och algoritmerna har implementerats i kontrollsystemet.

Resultatet från de olika simuleringarna och beräkningarna stämmer väl överens med teorin bakom algoritmerna. Säkerhetskravet är uppnått och systemet anses stabilt.

3

Nomenclature

B [T] Magnetic flux density

𝐵_𝑚 [S] Magnetizing susceptance

C s [F] Capacitance in snubber

dV/dtcrit [V/t] The maximum derivative of the voltage

dV/dtD [V/t] The normalized value of the maximum derivative of the voltage

d [m] Thickness of the iron in the transformer

f [Hz] Frequency

𝑓_𝑛𝑒𝑤 [Hz] Frequency

𝐺_𝑐 [S] Magnetizing conductance

I [A] Current

Harmonic

I [A] Harmonic current

Imax [A] Maximum current

measured

I [A] Measured current

circuit

Iopen_ [A] Current, open circuit test

it shortcircu

I [A] Short-circuit current

kd [Asm] Constant due to thickness of the stacking, the sheet and the hysteresis curve.

filter

L [H] Filter inductance

al leakageTot

L [H] Leakage inductance

Ploss [W] Eddy losses

eddy

Ploss_, [W] Eddy losses

hysteres

Ploss_, [W] Hysteres losses

thyrsitor

Ploss_, [W] Losses in the thyristor

winding

Ploss_, [W] Winding losses

circuit

Popen_ [W] Power, open circuit test

𝑅₁ [Ohm] Resistance equivalent circuit

ce ci filtercapa

R _tan [Ohm] Inner resistance in the filter-capacitance

ce c filterindu

R _tan [Ohm] Inner resistance in the filter-inductance

inner

R [Ohm] Inner resistance

R n [Ohm] Resistance nr n

RPT [Ohm] Temperature depended resistance

primary

r [Ohm] Resistance, primary winding

R s [Ohm] Snubber-resistance

ondary

r_sec [Ohm] Resistance, secondary winding

me measuredti

t [s] Measured time

periodtime

T [s] Period time

𝑉_𝐴 [V] Voltage, phase A

𝑉_𝐴𝑐 [V] Voltage, Control phase A

4

𝑉_𝛼 [V] Voltage, phase alpha

𝑉_𝛼𝑐 [V] Voltage, Control phase alpha

𝑉_𝐵 [V] Voltage, phase B

𝑉_𝐵𝐶 [V] Voltage, Control phase B

𝑉_𝛽 [V] Voltage, phase beta

𝑉_𝛽𝐶 [V] Voltage, Control phase beta

𝑉_𝐶 [V] Voltage, phase C

𝑉_𝐶𝐶 [V] Voltage, Control phase C

𝑉_𝑑 [V] Voltage, phase d

𝑉_𝑑𝑐 [V] Voltage, Control phase d

V n [V] Voltage at point n

circuit

Vopen_ [V] Voltage, open circuit test

imary

V_Pr [V] Primary voltage

ondary

V_sec [V] Secondary voltage

𝑉_𝑞 [V] Voltage, phase q

𝑉_𝑞𝑐 [V] Voltage, Control phase q

 [rad/s] Angle velocity

primary

x [Ohm] Primary, equivalent circuit

ondary

x_sec [Ohm] Secondary, equivalent circuit

circuit

Yopen_ [S] Admittance, open circuit test

measured

Z [Ohm] Impedance

phaseangle

 [rad] Phase Angle

 [A/Vm] Electric conductivity

r [As/Vm] Relative permeability

0 [As/Vm] Permeability

Abbrevations

AC Alternating Current

DC Direct Current

IGBT Insulated Gate Bipolar Transistor

WEC Wave Energy Converter

G Gate

K Cathode

A Anode

E Emitter

FPGA Field-Programmable Gate Array

PI-regulator Partial-Integrated regulator

PAC Programmable Automation Controllers

F The instrument amplifiers reinforce

∝ Safetyfactor

5

Contents

1. Introduction ... 7

2.Theory ... 9

2.1. The transformer ... 9

2.2. The thyristor ... 11

2.3. The inverter ... 13

3. LabVIEW ... 14

4. Switching the tap transformer ... 15

4.1. Option 1: Tap change using thyristors. ... 15

4.2. Option 2: Tap change using power flow stop and thyristors ... 17

4.3. Option 3: Tap change using two inverters. ... 18

5. Algorithm for On-Load Tap Change ... 20

6. The drivecircuit to the thyristor ... 20

6.1. Temperature protection ... 20

6.1.1. Design of the temperature circuit ... 21

7. Losses in the filter and transformer ... 22

8. Synchronization of the inverter with the grid ... 24

8.1. Stationary PI-regulator Controller ... 24

8.2. Stationary PI-regulator controller working with alpha, beta-transformation ... 25

8.3. Synchronous PI-regulator controller working with dq-transformation ... 25

8.4. Synchronization with help from the grid’s voltage zero crossing. ... 27

9. Trace and follow the gridfrequency ... 28

9.1. Option 1 ... 28

9.2. Option 2 ... 29

10. Simulation ... 30

10.1. Simulink ... 30

10.2. FPGA and the Module ... 30

11. Results ... 31

11.1. The Transformer: Equivalent circuit ... 31

11.2. Efficiency of the transformer ... 32

11.3. Calculated losses in the filter and the transformer ... 33

11.4. Efficiency tap change system ... 34

11.4.1. Tap change system with Thyristor control ... 34

11.4.2. Tap change system with Thyristor control and power flow stop ... 37

6

11.4.3. Tap change system with two inverters ... 38

11.5. Synchronization to the grid ... 38

11.5.1. Synchronization with alpha-, beta transformation ... 38

11.5.2. Synchronization with dq0-transformation ... 39

11.5.3. Synchronization with comparator and XOR-gate ... 40

11.6. Trace and follow the gridfrequency ... 41

11.6.1. Option 1 ... 41

11.6.2. Option 2. ... 42

11.7. Algorithm for the On-Load Tap Change system ... 43

11.8. The total interface to the user ... 45

12. Discussion ... 46

12.1. Losses in the filter and transformer ... 46

12.2. Tap change system ... 46

12.2. Control of the inverter ... 47

12.2.1. Synchronize the inverter with the grid ... 47

12.2.2. Trace and follow the gridfrequency ... 47

12.3. Algorithm for the On-Load Tap Change system ... 48

13. Conclusion ... 48

14. Future work ... 49

15. Acknowledgement ... 50

16. References ... 51

Appendix A ... 52

Appendix B ... 53

Appendix C ... 54

Appendix D ... 58

Appendix E ... 59

Appendix F ... 60

Appendix G ... 61

Appendix H ... 62

Appendix I ... 64

Appendix J ... 65

Appendix K ... 66

Appendix L ... 68

7

1. Introduction

The world´s energy system is today addicted to fossil fuels. 70-80% of the total consumed energy comes from oil or coal[1]. The combustion of oil and coal release heat which can be converted to electric or mechanic energy. A side affect of the combustion process is the production of the greenhouse gas carbon dioxide. The amount of carbon dioxide has due to this energy system increased in the atmosphere. The effects of our Nature due to a higher amount of carbon dioxide in the atmosphere is a question with a lot of different answers.

Strong evidence points an increasing temperature, increasing dusters, higher sea-level, drought and more extreme climate with larger, stronger storms, tornados etc. This climate change will affect millions of people and other living species. This is an important problem of our time and one reason why the need for clean, cheap and renewable energy is increasing. [2]

Another important point is the dwindling of the fossil fuels reserves. This results in increasing prices and lack of energy [1].

Human have been using streaming water in rivers etc for a long time, both to perform mechanical work and later converting the flowing waters kinetic energy to electrical energy [3]. The kinetic energy in the oceans has not been extracted large scale, even though it´s great potential. In recent years the research on this potential energy source has increased, and of lot of different wave-energy converters have been developed.

A technique developed at Uppsala University is a linear direct driven permanent magnet generator placed on the seabed. The wave’s kinetic energy is absorbed by a point absorbing buoy on the sea surface, directly connected to the generator, see Fig. 1.1. The movement of the waves moves the buoy and hence the translator, piston, up and down.

Figure 1.1: A schematic linear generator.

The choice to work with a direct driven generator is made to be able to eliminate mechanical part, gearboxes etc, as much as possible. By this choice, the generators have a robust construction and require minimal of maintenance.

8 The output voltage from the linear generator varies both in frequency and amplitude due to the movement of the waves. To be able to feed this output voltage to the national grid, the voltage is converted to a constant AC. To achieve this, a marine substation is added to the system, between the generators and the national grid, see Fig. 1.2.

Figure 1.2: Picture over a fictive wave park.

The first step in the substation is the rectifier. The rectifier consists of six passive components, diodes, and is not dependent of active control. The rectifier is followed by a large capacitor bank. The varying DC voltage charges the capacitors, and a stable DC voltage output can be reached. The stabilized DC voltage is converted to AC voltage with the desired frequency by an inverter. The inverter consists of six active electrical components, six IGBTs. These active components are dependent of control. A supplementary task for the control system are to synchronize the inverter with the local grid and follow the grid´s changing frequency. The last part of the conversion is to transform the voltage to suitable amplitude and by an LCL-filer reduce the amount of harmonics.

In different sea states the generator´s translator is moving up and down at different velocities.

To maximize the output power from the generator, the DC level will probably be different for different sea states. To investigate how the output power changes for different DC voltage levels, the transformer in the substation is a tap transformer. The tap transformer has five different taps, and five different primary voltage levels are available. By change of active tap, a different voltage level is activated and the generators are damped differently. To reach a smooth system, the tap change has to be performed without stop in the power flow.

The aim of this thesis is to investigate how a smooth and safe tap change can be achieved and to construct a control system for the inverter.

The report starts with a Theory part, where the main components in this work are described.

The format of the control system and three different on load tap change systems are presented.

Commercial methods used to synchronize the inverter with the grid are described with both its pros and cons.

The Result-part sums up and presents the different losses in the three different on load tap change systems. Simulation results from the different synchronization methods are available and drivecircuit for the electrical component are presented. The Discussion-part evaluates the advantages and disadvantages of the different system and methods.

9

2.Theory

2.1. The transformer

In the substation a tap transformer with five taps on the primary side is used to reach the wanted voltage level at 1 kV.

The equivalent circuit of the transformer is shown in Fig. 2.1.

Figure 2.1: The equivalent circuit of the transformer.

To achieve simulated result as close to reality as possible, the transformer’s equivalent circuit was calculated. The basic parameters are calculated by:

𝑎 =_𝑉^{𝑉𝑝𝑟𝑖𝑚𝑎𝑟𝑦}

𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 (2.1)

𝑅₁ = 𝑟_{𝑝𝑟𝑖𝑚𝑎𝑟𝑦} + 𝑎²𝑟_{𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦} (2.2)

𝑋₁ = 𝑥_{𝑝𝑟𝑖𝑚𝑎𝑟𝑦} + 𝑎²𝑥_{𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦} (2.3)

The parameter 𝑅₁, is obtained by measuring the resistance in the primary and secondary winding, and the parameter,𝑋₁, by measuring the impedance across one of the winding terminals when the other is short circuited.

𝑍_{𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑} = 𝑅₁²+ 𝑋₁² → 𝑋₁ = 𝑍₁² − 𝑅₁² = 𝑥_{𝑝𝑟𝑖𝑚𝑎𝑟𝑦} + 𝑎²𝑥_{𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦} (2.4) 𝑥_{𝑝𝑟𝑖𝑚𝑎𝑟𝑦} ≈ 𝑥_{𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦} ≈^𝑋₂¹ = 𝑤𝐿𝑙𝑒𝑎𝑘𝑎𝑔𝑒 𝑇𝑜𝑡𝑎𝑙 (2.5)

By applying the rated voltage at one of the transformer terminals, the parameters Gc and Bm

are found. The induced current was measured and the circuit admittance was calculated. [4]

𝑃𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡 = 𝑈𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡𝐼𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡 (2.6)

𝑌𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡 = ^𝐼𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡

𝑈𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡 (2.7)

𝑈𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡2 𝐺_𝑐 = 𝑃𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡 → 𝐺_𝑐 =^𝑃𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡

𝑈𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡2 (2.8)

r_primary x_primary

Gc Bm

a²x_secondary a²r_secondary

10 𝑌𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡 = 𝐵_𝑚² + 𝐺_𝑐² → 𝐵_𝑚 = 𝐺𝑐2− 𝑌𝑜𝑝𝑒𝑛 −𝑐𝑖𝑟𝑐𝑢𝑖𝑡2 (2.9)

If all taps on the transformer are wound with the same material, each tap-coil contributes the same amount of leakage inductance as it´s corresponding percent size of the transformers total coil. Each tap´s leakage inductance can then be calculated according of Eq. (2.10).

𝐿𝑙𝑒𝑎𝑘𝑎𝑔𝑒 ,𝑇𝑎𝑝 𝑛 = _𝑉^{𝑉𝑇𝑎𝑝}

𝑇𝑜𝑡𝑎𝑙 𝐿𝑙𝑒𝑎𝑘𝑎𝑔𝑒 𝑇𝑜𝑡𝑎𝑙 (2.10)

11 2.2. The thyristor

The electrical symbol for the thyristor is shown in Fig. 2.2. A thyristor can both conduct and block power and can be used to control the power flow to the different taps on the transformer.

Figure 2.2. The electrical symbol for a thyristor.

A thyristor starts to conduct when an activating signal appear on its gate.

When the thyristor is activated, it stays in a conducting position, as long as the voltage over the component is positive and the current size is higher than the thyristor´s threshold value. A thyristor give rise to losses due to inner resistance and created harmonics. [5]

𝑃𝑙𝑜𝑠𝑠 ,𝑡𝑕𝑦𝑟𝑖𝑠𝑡𝑜𝑟 = 𝐼²𝑅_{𝑖𝑛𝑛𝑒𝑟} + 𝐼_{𝐻𝑎𝑟𝑚𝑜𝑛𝑖𝑐} 𝑈 (2.11)

2.2.1. Safety

A thyristor is not capable of withstand a too large amplitude or too great change of current or voltage. To protect the thyristor, a safety circuit, a snubber, is added in parallel. In our case, a RC-snubber is suggested, see Fig. 2.3. [6]

Figure 2.3: The thyristor with the RC- snubber connected in parallel.

To design a snubber optimized for each specific case a damping factor, D, is specified. The value of the damping factor decides the priority of the protection. A high damping factor priorities the protection against voltage, and a low value priorities the protection against a too large variation of the voltage. A normal value for an optimal protection for both is D=0.4 [6].

The value of the resistance and capacitance can be calculated from the following equations [5]:

𝑤_𝑜 = ^{𝑑𝑉 𝑑𝑡 𝑐𝑟𝑖𝑡𝛼}

𝑑𝑉 𝑑𝑡

𝐷𝑈 (2.12)

𝐶_𝑠 = _𝑤 ¹

𝑜2𝐿_{𝑓𝑖𝑙𝑡𝑒𝑟} Eq. (2.13)

Rs

C_s

12 𝑅_𝑠 = 2𝐷 ^{𝐿𝑓𝑖𝑙𝑡𝑒𝑟}_𝐶

𝑠 (2.14)

13 2.3. The inverter

The inverter is constructed with help of six IGBTs.

The electrical symbol for the IGBT is shown in Fig. 2.4. Similar to the thyristor, the IGBT can be used to both conduct and block power [7].

Figure 2.4: The IGBT with a diode connected in parallel

The IGBTs in the inverter have to be switched on and off in a specific pattern in order to generate the required alternating voltage. Simultaneous feeding a sine-wave and a saw-tooth wave into the comparator, the required switching pattern can be created, se Fig. 2.5.

Figure 2.5: The switching pattern creates of the sine-wave and the saw tooth wave.

When the sine-wave is larger than the saw-tooth wave, the comparator delivers a high output and vice verse. The output from the comparator will be the created switching pattern.

14

3. LabVIEW

To receive a nice sinusoidal AC voltage out from the inverter, a high switching frequency is required. A high switching frequency puts high demand on the operation speed of the controlsystem.

LabVIEW is a software computer program how offers the user an opportunity to program code graphical with the help of block diagrams. Hundreds of built-in catalogs with mathematical, logical gates etc and can be integrated with thousands of different kind of hardware devices. The code can be written in different subpart, where each part has different properties. Two of these subparts are the FPGA and the Real Time.

The FPGA can export and import analogue and digital data with an operating speed in the microsecond level (8). With the FPGA, the demanded operation speed of the controlsystem can be reach. The FPGA can however not perform unlimited number of mathematical calculations when the operation speed is in the microsecond level. The amount of calculations is decided of the current operation speed and the maximal operation speed.

The code written in the FPGA can be controlled by a Host-code, created in the Real Time. A connection between the two subparts will hence exist. Calculation and operation which the FPGA is not capable to perform can by the connection be sent and performed in the Real Time, see Fig. 3.1. [8]

Figure 3.1: The information transported between FPGA and Real Time.

The main tasks for the studied controlsystem are:

 Activate and de-activate the IGBTs in the specific switching pattern.

 Synchronize the inverter to the grid.

 Make sure the inverter´s frequency follows the grid´s changing frequency.

 Offer a safe tap change.

15

4. Switching the tap transformer

To investigate how the output power changes for different DC voltage levels, the transformer in the substation is a tap transformer with five different taps. By change of active tap, a different voltage level is activated and the generators are damped differently. To reach a smooth system, the tap change has to be performed without a stop in the power flow.

Three different tap change systems are here investigated.

4.1. Option 1: Tap change using thyristors.

The first suggested tap change system, includes tap control by two anti-parallel thyristors [10].

A tap change from Tap 5 to Tap 4 is performed as follow:

1. The thyristor-pair of Tap 5 is activated and conducts, see Fig. 4.1 a).

2. The thyristor-pair of Tap 4 activates and starts to conduct. The two taps are now shortcircuited, see Fig. 4.1 b).

3. The thyristor-pair which controls Tap 5 de-activates. The two anti-parallel thyristors stops to conduct when the current reaches below the threshold value, see Fig. 4.1 c).

4. A tap change is performed.

Tap change between other taps performs in the same way. [10-14].

Figure 4.1: a ) Tap 5 is active. b) Tap 5 and Tap 4 is active. c) Tap 4 is active.

By activating the thyristor-pair of Tap 4´s in the same time as the Tap 5´s thyristor-pair is de- activated, the theoretical short-circuit time is zero. This is however not true in practic. A thyristor has a turn off time in the order of 100 microseconds. During these 100 microseconds, the two taps are short-circuited. The two short-circuit taps is a closed circuit and a large short- circuit current is induced by the magnetic field which flows through the transformer, according to Ampere´s law of induction [15]:

𝐵

𝜇0𝜇𝑟𝑑𝑟 = 𝐼𝑠𝑕𝑜𝑟𝑡𝑐𝑖𝑟𝑐𝑢𝑖𝑡 (4.1)

There is a risk that the short-circuit current becomes larger than the thyristor´s threshold value. If that would be the case, the thyristor is no longer capable to de-activate and remain in conducting position for half a period. The system has to be able to handle the large short- circuit current, and current-limited inductors are hence located before each thyristor-pair. The size of the short-circuit current dimensions the current-limited inductors. [11-12, 14]

This option became a space-demanding and costly alternative, see Fig. 4.2.

16 Figure 4.2: The circuit with the thyristor system.

17 4.2 . Option 2: Tap change using power flow stop and thyristors

The previous option´s main drawback was the space-demanding and the costly filters. If the tap change is performed under a power flow stop, filter on each tap is no longer required.

[10, 13].

A tap change from Tap 5 to Tap 4 is performed as follow:

1. The thyristor-pair of Tap 5 is active and conducts, Fig. 4.3 a).

2. The active thyristor-pair de-actives, Fig 4.3 b).

3. The thyristor-pair which controls Tap 4 activates a half period later, Fig. 4.3 c) 4. A tap change is performed.

Figure 4.3: a) Tap 5 is active b) No tap is active c) Tap 4 is active

No taps are short-circuited and no short-circuit current is created. The short-circuit current- limiting inductors can be removed, and the system is only depended on one filter [10].

Fig. 4.4 presents the different location of the filter.

Figure 4.4: a) The LC-filter before the transformer b) The CL-filter after the transformer.

This system is however not smooth and cannot offer an on load tap change.

18 4.3. Option 3: Tap change using two inverters.

An option, completely different from the two previous presented, is the possibility to use two inverters, and by a contactor control the power flow through the different taps, see Fig 4.5.

Figure 4.5: The circuit with the two inverter system, and the filter located after the transformer.

A tap change from Tap 1 to Tap 2 is performed as follow:

1. Inverter A and the contactor which controls Tap 1 on the transformer is active, Fig. 4.6 a).

2. The contactor to Tap 2 closes, and is ready to conduct when Inverter B activates, Fig.

4.6 b).

3. Inverter A de-activates at a zero crossing voltage, and Inverter B activates in less than a microsecond-interval, Fig. 4.6 c).

4. Contactor to Tap 1 de-activates, Fig. 4.6 d).

5. A tap change is performed.

19 Figure 4.6: A schematic picture of a tap change.

With help of the controlsystem, the change of active inverter can be done in less than a microsecond. The microsecond change implies that no power flow stop is necessary.

Tap change between other taps is performed in the same way, with the constrain that a safely tap change only can be performed between taps connected to different inverters.

20

5. Algorithm for On-Load Tap Change

How the algorithm for this system is created, depends on which of the 3 tap change system that is chosen. The only common demand of the different systems is the desire to minimize the strain and the safety risk to the total system.

The IGBT in the inverter has a diode connected in parallel to it. If the voltage level is higher on the AC side of the inverter than the DC side, this diode conducts. To avoid a large current flowing through the diode back to the DC side, and thus risk the IGBTs safety, the AC voltage can never be higher than the DC voltage. An extra safety system has hence been added. If the selected tap represents an AC voltage higher than the instantaneous DC voltage, the tap change can not be performed. For written code, see Appendix A.

6. The drivecircuit to the thyristor

The thyristor is like the inverter controlled with help of a controlsystem written in LabVIEW.

With help from the control system, the user can demand the thyristor to activate and conduct power. The user´s demand results in a high voltage signal at the Module´s Digital Output. To transport the high voltage signal from the Module to the thyristor´s gate, a drivecircuit is used.

The heart of the drivecircuit is the driver. In this model, driver IR2121 is suggested. When the user demands the thyristor to activate, the driver is activated and a trigger signal is send to the thyristor. The driver is hence both connected to the Module and the thyristor. The Module is here in-directly connected to the main powerflow line in the substation through the driver.

This creates a huge risk of safety, and cannot be allowed, due to the Module´s sensitivity.

To protect the Module and controlsystem from the high power flow in the substation, an opto- coupler is attached, placed between the signal from the Module and the driver. The voltage signal from the Module is now received by the opto-coupler. The opto-coupler converts the voltage signal to a light beam which in turn activates a transistor. The powerflow through the transistor activates the driver. By this conversion, the two systems are totally electrically isolated from each other.

6.1. Temperature protection

To protect the thyristor from heat, a temperature protected circuit has been added to the drivecircuit. The suggested design includes an instrument amplifier and a comparator, see Fig.

6.1.

21 Figure 6.1: The instrument amplifier and the comparator.

The temperature protected circuit uses a temperature depending resistance, R15 in Fig. 6.1.

When the thyristor reaches its specified maximum temperature, the circuit shall be designed so U3 reach a value greater than U4. The comparator activates and results in an output voltage signal, U5. The output from the comparator is connected to the driver’s error-input. When a high voltage appears at the error-input, the driver automatically shuts down.

6.1.1. Design of the temperature circuit

To minimize the number of elective parameters, the resistances R11, R12, R13, R14, R5 and R6

got fix values:

R₁₁=R₁₂=R₁₃=R₁₄=1000 Ohm U₀ =10 V R5= 10 kOhm and R6= 5 kOhm U4 =5 V

The resistance PT1000 was suggested as the temperature depended resistance.

PT1000 has a temperature coefficient 3850 ppm/K with a resistance value at 1000 Ohm at zero degree.

0 1000

, _C 

RPT Ohm

10

* 3850

* 1000

, n*

R_PTnC  ^-6+1000 Ohm (6.1)

The voltage U₁ and U₂ describes as:

𝑈₁ = _𝑅 ^𝑅11

11+𝑅𝑃𝑇𝑈₀ (6.2)

𝑈₂ =_𝑅 ^𝑅13

13+𝑅12𝑈₀ (6.3)

22 The potential difference between U₁ and U₂ and the instrument amplifiers enhanced describe𝑈₃:

𝑈₃ = (𝑈₂− 𝑈₁ ) ∗ 𝐹 (6.4)

When the temperature increases, the temperature depended resistance increase and the voltage U₁ decrease. At the maximum allowed temperature, a specific voltage difference between U₁ and U2 is reached.

∆𝑉_{𝑚𝑎𝑥 ,𝑡𝑒𝑚𝑝} = 𝑈₂− 𝑈₁ (6.5)

This voltage difference has to be enhanced to a greater value than U₄ by the instrument amplifier.

𝐹 =_∆𝑉 ^𝑈4

𝑚𝑎𝑥 ,𝑡𝑒𝑚𝑝 (6.6)

At the maximum allowed temperature, U₃ is hence larger than U₄. [17]

7. Losses in the filter and transformer

To reduce the amount of harmonics in the line, a LCL-filter is included in the system. The losses in the filter describes as:

𝑃𝑙𝑜𝑠𝑠 𝑓𝑖𝑙𝑡𝑒𝑟 = 𝐼²𝑅𝑓𝑖𝑙𝑡𝑒𝑟 𝑖𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 + 𝐼_{𝑕𝑎𝑟𝑚𝑜𝑛𝑖𝑐}² 𝑅𝑓𝑖𝑙𝑡𝑒𝑟 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 (7.1)

Eq. (7.1) illustrates that the losses increase with increasing value of the current. The losses in the filter are hence greater if it is placed on the primary side of the transformer.

The transformer gives rise to losses of its own. These losses have mainly three sources:

𝑃𝑙𝑜𝑠𝑠 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑒𝑟 = 𝑃𝑙𝑜𝑠𝑠 ,𝑤𝑖𝑛𝑑𝑖𝑛𝑔 + 𝑃_{𝑙𝑜𝑠𝑠 ,𝑒𝑑𝑑𝑦} + 𝑃𝑙𝑜𝑠𝑠 ,𝑕𝑦𝑠𝑡𝑒𝑟𝑒𝑠 (7.2) The power loss in the winding is described as:

𝑃𝑙𝑜𝑠𝑠 ,𝑤𝑖𝑛𝑑𝑖𝑛𝑔 = 𝑅𝐼² (7.3)

The size of the eddy current losses can be calculated by:

𝑃_{𝑙𝑜𝑠𝑠 ,𝑒𝑑𝑑𝑦} = 𝜋^𝜎𝑑₆² 𝐵𝑓 ² (7.4)

The size of the hysteresis losses is calculated by: [16]

𝑃𝑙𝑜𝑠𝑠 ,𝑕𝑦𝑠𝑡𝑒𝑟𝑒𝑠 = 𝑘_𝑛𝐵²𝑓 (7.5)

Due to Eq. (7.4) and Eq. (7.5), both the eddy- and hysteresis losses are dependent on the frequency. The losses in the transformer will rise if the voltage includes a lot of harmonics,

23 i.e. the filter is located after the transformer, [16]. Calculations for both the losses in the filter and transformer have to be done, to optimize the location of the filter.

24

8. Synchronization of the inverter with the grid

To connect the wave power park to the local grid, the inverter has to be synchronized to the grid. The AC-voltage created by the inverter must have the same phase, the same voltage- amplitude and the same frequency as the AC-voltage in the grid [3].

The ability to synchronize the inverter with the grid is based on the opportunity to change the control signal to the inverter. The change of the control signal can be done in several ways, and some of them are presented in this chapter.

8.1. Stationary PI-regulator Controller

One of the simplest methods to synchronize the inverter to the grid is to use a Stationary PI- regulator Controller, see Fig. 8.1.

Figure 8.1: The circuit of synchronize the inverter with the grid with help of Stationary PI- regulator Controller.

The measured voltage from the three phases of the grid is compared with the measured voltage from the three phases after the inverter. The difference between them is calculated, and the error enters a PI-regulator. The output from the PI-regulator is added to the inverters control signal. By this method the control signal changes relatively easy. However, the method has some drawbacks. Due to its simplicity, the comparison is not optimal, and a non- zero error is hard to reach. To be able to minimize the error to zero, some mathematical tools can be used [18].

25 8.2. Stationary PI-regulator controller working with alpha, beta-transformation

As said before, the ability to synchronize the inverter with the grid bases on the opportunity to change the control signal to the inverter. The change has to be done due to how the output voltage from the inverter behave relative the grid voltage.

To be able to do a fast and smooth comparison, the measured voltages after the inverter and from the grid is transformed. The three phases A, B and C are converted to two phases, alpha- , beta- stationary coordinates, with help from Clark’s transform [4].

The transform can be described as:

This transformation can be used in the Stationary PI-regulator controller [18].

The measured voltages are transformed to alpha- and beta coordinates, and compared with each other. The difference, the error, between the two signals are calculated and sent into the PI-regulator. The output from the PI-regulator, is transformed back to three phases and added to the control signal, see Fig 8.2. A new changed control signal has been created. [18]

Figure 8.2: The circuit of synchronize the inverter with the grid with help of Stationary Controller PI working with alpha, beta transformation.

8.3. Synchronous PI-regulator controller working with dq-transformation

The result of the alpha-, beta transformation can theoretically not reduce the error between the two measured signals to zero. To be able to reduce the error to zero, the two voltage measurements have to be transformed one step further. They have to be transformed with the dq0-transformation.

( 8.1)

26 By the dq-transformation, the stationary alpha-, beta-coordinate converts into a rotating coordinate system and is expressed as a d- and a q-vector.

The transformation can be described as:

The transform from the three A, B and C phases to d-, q- vectors can be expressed in one step (19):

The

The transform from d-, q- vectors to the three A, B and C phases can be written as: [4]

The rotating d- and q-vectors offer a better chance to perform an optimal comparison between the two measured signals than the sinusoidal three phases A, B and C or the sinusoidal two phases alpha, beta offered. A theoretical error equal to zero can be reached.

This transform can be used in the synchronize method, ’Synchronous PI controller working with dq-transformation’, see Fig 8.3. [18]

(8.4) (8.3) (8.2)

27 Figure 8.3: The circuit of the synchronize working with dq- transformation.

The measured voltages are transformed to d- and q-vectors, and compared with each other.

The different, the error, between the two signals are calculated and sent into the PI-regulator.

The output from the PI-regulator transforms back to three phases and is added to the control signal to the inverter. A new changed control signal has been created. [18]

8.4. Synchronization with help from the grid’s voltage zero crossing.

An option, different from the three previous presented synchronize option methods, is the possibility to turn on the inverter when the grid´s voltage passes zero. As long as the inverter and the grid have the same frequency, a synchronization due to phase is reached.

To find the grid zero crossing voltage, the grid measuring signal is converted to a square wave with help of a comparator. As long as the voltage is greater than zero, the comparator delivers a high signal. When the voltage becomes less than zero, the comparator turns and starts to deliver a low signal, a zero.

The comparator is connected to a XOR-gate, see Fig. 8.4.

Figure 8.4: A comparator connected to an XOR-gate.

An XOR-gate delivers a low value, a zero, as long as the values on its two inputs are equal.

When the value on its two inputs differs, the XOR-gate delivers a high value. [19]

28 By compare the newest with the previous output value from the comparator in the XOR gate, the XOR-gate deliver a high value when the grid voltage crosses zero. The high value activates the controlsignal to the inverter. The required amplitude is obtained by the modulation index.

When the inverter has been activated, this algorithm is not needed, and is turned off.

9. Trace and follow the gridfrequency

The grid´s frequency is allowed to be in the interval [49.95 – 50.05 Hz] [3]. To keep the inverter in phase with the grid, the inverter has to follow the grid’s frequency. The grid’s instantaneous frequency has to be found and implemented in the controlsignal to the inverter.

The inverter original set is to convert DC-voltage to a 50 Hz AC-voltage. If the grid voltage drops to 49.95 Hz, the inverter output voltage oscillates faster, and a negative phase angle due to the grid appear. The output current and voltage from the inverter is affected differently of this phase angle, and a phase angle relative the output current and voltage from the inverter is created. By investigating the phase angle between the output current and voltage from the inverter, the change in the phase angle relative the grid, and hence how the frequency change, can be found.

Both the current and voltage is measured in the substation, and is available to the controlsystem. There are two main options to control the phase angle between the voltage and current. Both options have its pros and cons.

9.1. Option 1

The first way to investigate the phase angle is performed as follow:

Every time the measured voltage passes zero from the negative side, a mathematical algorithm is activated. The activated mathematical algorithm measures the instantaneous current amplitude. Since the maximum value of the current is known by resent measurement, its phase angle relative the voltage can be expressed as follow:

𝐼_{𝑚𝑒𝑎𝑠𝑢𝑟𝑒} = 𝐼_𝑚𝑎𝑥 sin(𝛿_{𝑝𝑕𝑎𝑠𝑒𝑎𝑛𝑔𝑙𝑒} ) (9.1)

If 𝛿_{𝑝𝑕𝑎𝑠𝑒𝑎𝑛𝑔𝑙𝑒} is small, <^𝜋₄, Eq. (9.1) can be rewritten as: [20].

𝐼_{𝑚𝑒𝑎𝑠𝑢𝑟𝑒} = 𝐼_𝑚𝑎𝑥𝛿_{𝑝𝑕𝑎𝑠𝑒𝑎𝑛𝑔𝑙𝑒} → 𝛿_{𝑝𝑕𝑎𝑠𝑒𝑎𝑛𝑔𝑙𝑒} = ^{𝐼𝑚𝑒𝑎𝑠𝑢𝑟𝑒}_𝐼

𝑚𝑎𝑥 (9.2)

The percentage displacement can be found by

𝛿𝑝 𝑕 𝑎𝑠𝑒𝑎𝑛𝑔𝑙𝑒

2𝜋 = 𝑋% (9.3)

To minimize the risk to do a too great change, only 10 % of the percentage error will be used as a source for the change in frequency.

Y=^𝑋%₁₀ (9.4)

29 The new frequency sent to the inverter will hence be:

fnew =50*Y + 50 Hz (9.5)

9.2. Option 2

A second way to determine the phase angle is here presented:

The algorithm measure the time between the voltages zero crossing point and the current zero crossing point. Since the period time is known, the percentage displacement can be found:

𝑡𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑡𝑖𝑚𝑒

𝑇_{𝑝𝑒𝑟𝑖𝑜𝑑𝑡𝑖𝑚𝑒} = 𝑋% (9.6)

To minimize the risk to do a too great change, only 10 % of the percentage wrong will be used as a source for the change in frequency.

Y=^𝑋%₁₀ (9.7)

The new frequency sent to the inverter will hence be:

fnew =50*Y + 50 Hz (9.8)

In both the two options, only 10 % of the displacement work as a base for the change of the frequency. A delay in the change of the inverter’s frequency appears. A phase angle is created due to the different oscillation time between the grid voltage and the inverter under this delay.

This phase angle remains even when the frequency has stabilized. To be able to reduce this phase angle, a P-regulator has been implemented in the algorithm. As long as an unwanted phase angle exist, the P-regulator makes sure that the controlsignal´s frequency changes, a very small but still appreciable change, until the unwanted phase angle is reduced.

30

10. Simulation 10.1. Simulink

To test and investigate the different models without the need of a real system, a simulation program is used. One program in question is Simulink.

Simulink is a simulation program integrated with the software program MATLAB. The program offers the user to graphical write code with pre-installed blocks. Simulink includes specific toolboxes with a great amount of electrical component. Electrical circuits can be build, simulated and analysed. The integration with MATLAB gives the user opportunity to both import and export specific data. This is very useful when specific circuits are tested with specific measurements.[9]

10.2. FPGA and the Module

Simulink give the user an opportunity to simulate and investigate different algorithms.

However, the software program cannot integrate with hardware in the way that is necessary to investigate the speed and ability for some of the algorithms. Experiments were hence also performed with help from FPGA and the Modules.

With help from the Analog Input Module a sine-wave, created by a signal generator became measured and available in the computer. At the time the experiments were performed, no inverter was available. A sine-wave created in LabVIEW had to act as the output from an inverter. Both the measured signal from the function generator and the activated sine-wave from LabVIEW became available on the Digital Output Module, and plotted on the

oscilloscope. Due to the fact that the Digital Output Module is used, the sine-waves were converted to square-waves. The square-waves will rise and fall when the sine-waves crosses zero.