Assessment of 42 Km, 150 kV AC submarine cable

at the Horns Rev 2 HVAC wind farm

Electrical Energy Engineering

EPSH 3, Group 901, Fall Semester 2010

Department of energy Technology, Aalborg University

2

TITLE:

“ASSESSMENT OF 42 Km, 150 kV AC SUBMARINE CABLE”

SEMESTER: 3RD

SEMESTER EPSH (M.SC) PROJECT PERIOD: 15.09.2010 – 04.01.2011 ECTS: 22 SUPERVISOR: FILIPE MIGUEL FARIA DA SILVA CLAUS LETH BAK PROJECT GROUP: EPSH 3, GROUP 901

ANGEL FERNÁNDEZ SARABIA

CAROLINA ARAGÓN ESPALLARGAS

COPIES: 3 PAGES, TOTAL: 85 APPENDIX: 1 SUPPLEMENTS: PROJECT CD

BY SIGNING THIS DOCUMENT, EACH MEMBER

OF THE GROUP CONFIRMS THAT ALL

PARTICIPATED IN THE PROJECT WORK AND

THEREBY THAT ALL MEMBERS ARE COLLECTIVELY

LIABLE FOR THE CONTENT OF THE REPORT.

SYNOPSIS:

The aim of this project is to investigate the

measurement results presented in a preliminary report,

by comparing them with a model created in PSCAD

EMTP. The investigation is based on the transmission

line that electrically connects the offshore wind farm

Horns Rev II with the onshore substation at Endrup. A

model of part of the transmission line will be developed

in PSCAD EMTP. Once the results are studied, an analysis of the

submarine cable that is causing the mismatch between

simulations and measurements is performed. This

analysis has been made using a finite element software

and theoretical equations.

Based on this analysis an improved model of the

submarine cable will be designed. Furthermore,

simulation results will be compared against

measurements results and equations results.

Comparison between the simulation model and the

analytical results shows a good agreement. This

indicates that the proposed study method is valid.

On the other hand, comparison between simulation

model and measurements results shows a large

deviation. The Ferranti effect simulated is 1.6% while in

the measurements is 8%. Furthermore, the simulated

voltage at the receiving end is bigger than the one

obtained in the measurements. This is caused by the

capacitors introduced at the end of the system as a way

to improve the model, which are increasing the

voltage of the whole system.

3

Content

1. Introduction………………………………………………….5

2. System description………………………………………..7

2.1 Turbines………………………………………………8

2.2 Cables………………………………………………….8

2.3 Grounding of the cable………………………..14

2.4 Connection of the subsystems……………..16

3. Problem analysis………………………………………………18

3.1 Cable models………………………………………18

3.2 Problems associated during the energization of the cable……20

3.3 Problems in steady state………………………………………………………….29

3.4 Effect of the cable on the grid…………………………………………….32

3.5 Problem statement……………………………………………….33

3.6 Aim of the project…………………………….34

3.7 Solution method……………………………………34

4. Comparison between theory equations and PSCAD results…………….35

4.1 Submarine cable model in PSCAD…………………………………………35

4.2 Receiving end voltage of each configuration………………………..37

5. Description of the PSCAD model………………………………………..49

5.1 PSCAD model configuration………………………49

5.2 Choice of the cable……………………..49

5.3 Land cables and submarine cable…………………..50

5.4 Voltage source and short circuit impedance………………..56

5.5 Circuit breaker………………………57

4

5.6 Shunt reactor…………………………………60

5.7 Simulation settings……………………………65

6. Results and validation of the model……………………..66

6.1 Results of the improved model in PSCAD……………..66

6.2 Analysis of the pipe type cable model……………..67

7. Conclusions……………………………………………………….72

7.1 Future work………………………………………….73

8. Literature………………………………………………….74

A Appendix submarine cable parameters calculation……………….79

5

1. Introduction

Nowadays Denmark is able to cover approximately the 20 per cent of its energy

demand with wind energy. Due to the higher allowance for CO2 and oil prices, its aim is

to achieve the long objective of increasing the wind production to 50 percent by 2025.

Part of this expansion will occur through the use of offshore wind farms. [1]

Denmark is a small country that has taken advantage of its long coastline with the

terms offered by an offshore installation such as: better wind resources (the marine

wind are more stables with less turbulence and less wind shear), larger spaces to

install the wind farms and lower environmental impact. [2]

Countries such as Germany, China, Netherlands, Ireland, United Kingdom, Norway,

Finland, Japan and Netherlands have offshore technology , but Denmark was the

pioneer country installing its first offshore wind farm Vindeby ( 4.95 MW). Its path has

continued with others nine farm until 2009 with the setting of the largest offshore

wind park Horns Rev II (209 MW). [3]

Horns Rev II (HR2) is an offshore wind farm which is located 30 km far from the shore,

in the North Sea. The produced power in the offshore station is transmitted to the

onshore station, through 99.7 kilometers of buried cable. The first 42 km of submarine

cable, are connected with 57.9km of land cable. [4]

The offshore wind park is connected to land in three parts: a transformer platform, a

sea cable and a land cable. In the transformer platform the voltage from the wind

turbines is increased up to 150 kV, nominal voltage of the AC transmission cable.

A high voltages underground cable presents higher capacitance than overhead lines.

The insulation materials act as a capacitor, so a large part of the current is used as a

charging current of the capacitance of the line. Hence, a lower active power flow can

be transferred to the grid. This fact forces to use shunt reactors, as inductive

components, in parallel along the power grid for compensating the reactive power

produced. [27]

During the energization of a long HVAC cable, occurs a transitional state that can

exceed the maximum values of voltage and current for which the components were

designed. These overvoltages and overcurrents, despite being instantaneous, can

damage system components. [32]

Energinet.dk, the owner of the electrical connection of the wind park, asked Siemens

a report regarding overvoltages at the connection. Due to Siemens supplies a little

6

information about the models of the cables used, (the choice of model has

considerable influence on the results of the simulation) the simulations were repeated.

In the report “Studies of transient overvoltage at the Horns Rev 2 wind farm HVAC

cable connection” was concluded that the overvoltages measurements were in

agreement with the simulations during the switching on. On the other hand, the

relative permittivity for the main insulation material must be recalculated correctly in

order to take into account the semiconducting layers of the cable. [18]

The “Full Scale Test on a 100km, 150kV AC Cable” shows a large Ferranti effect (8%) in

the measurements, while in the simulation results the voltages in the sending and in

the receiving end are similar (an increase of 1.7%). Furthermore, it was noticed during

the de-energization, differences between the simulation and the measurement, even

in steady state. [5]

Because of the time limitation, the aim of this project is focused on the study of the

steady state behavior of the transmission system taking into account where and how it

can be improved.

7

2. System description

In this chapter a description of the system is made.

Introduction

Horns Rev 2 is a big construction formed by many sub-systems that globally

form the whole structure. Its construction was a very big challenge because was the

furthest offshore wind farm built in the world.

The construction period was from May 2008 to November 2009. It was inaugurated in

September 2009, a few months before the climate conference took place in

Copenhagen in December.

The HR2 is managed by the national grid network operator Energitek.dk, who plans

and controls the peaks on the wind power supply and also when the wind drops,

looking for other available energy sources. [4]

The park is situated outside the west cost of Denmark at 30 km from the coast line,

where water depth is 9-17 metres and the average wind speed is just below 10 m/s.

The average wave height is 1.5 metres. This location is shown in the next figure.

Fig. 2.1 Location of the offshore wind park Horns Rev 2. [Bilfinger Berger Magazine

2/2008]

8

The owner is DONG Energy and coordinates the complete process with seven different

sub-companies. DONG Energy is one of the leading energy groups in Northern Europe.

Its business is based on supporting, producing, distributing and exchanging in energy in

Northern Europe.

2.1 Turbines

The wind farm is formed of a total of 91 wind turbines, with a unitary capacity of 2.3 MW each one, so the total production capacity is of 209 MW. These turbines are supplied by Siemens and are of the type SWP 2.3-93. The centre point of the blade was placed 68 metres above the sea level. The length of

the turbine below sea level is between 30-40 metres. With a blade diameter of 93

metres the total length of the wind turbine above the sea level is 114.5 metres.

The erection of these turbines was carried out with a number of different special built

vessels. Each turbine is able to communicate between the shore and the

accommodation platform though its IP number which sets the connection.

Fig.2.2 Wind turbines in Horns Rev 2. [4]

2.2 Cables

A total of 70 km of cables were laid out at Horns Rev 2. These cables are

connected between the 13 rows of wind turbines from west to east, where they are

connected to the transformer platform, containing fibre network which transmits

communication and control to and from the wind turbines. [4]

9

Submarine system cable transports the produced electricity to the shore.

Fig. 2.3 Distribution of the 13 rows of wind turbines. [4]

10

2.2.1 Submarine Cable

The submarine cable used for Horns Rev 2 has a length of 42 km and is 150 kV

3x630 mm2.The cable is buried 1.3 m under the sea bed [Energinet.dk]. The

manufacturer is Nexans and the following data is taken from its datasheet.

The layout of the submarine is shown below:

Fig. 2.4 Layout of the submarine cable. [31]

In the next table are detailed the features of the materials and the outer radius

11

Table 2.1 Submarine cable data [31]

The cable is formed by three phase cables where the three conductors are placed in

common metallic armour. Each phase is formed by copper conductors with a cross

section of 630 mm2. Copper allows small cross section, requiring less material in the

manufacture of the conductors. Aluminium can be also used but, due to copper has a

higher corrosion resistance it is commonly used for submarine cables. [15]

The phase conductors have an insulation layer of cross linked polyethylene (XLPE) of

18 mm of thickness. [31]

A layer of semi-conducting XLPE is extruded onto the conductor in order to avoid voids

and irregularities, which can create a local stress and would reduce the insulation

dielectric strength. This semi-conductive layer is completely circular and has a smooth

surface; therefore, there will not appear stress increases. Another semi-conductive

layer outside the insulation, called insulation screen is provided in order to form a

stable dielectric surface not being affected by the outer screen layer. These layers:

conductor screen, insulation and insulation screen are the cable dielectric system. [15,

pg 34]

The metallic screen has a major importance due to nullify the electric field outside the

cable. It acts as a second electrode of the capacitor formed by the cable. On the other

hand, when an alternating current is flowing through a conductor of a cable, some

voltage will be generated on the screen. This voltage can reach several of volts during

normal operation. Therefore, sheath voltage limiters (SVL) are used between the

sheath screen and ground in order to limit this potential. [40, pg 13]

The humidity reduces the dielectric strength and the ageing resistance of the cable.

Due to this is necessary that the protection of the cable includes a swelling tape and a

lead alloy sheath. The swelling tape is a polyester fibre, which has the function of

12

expanding after it gets wet, s reducing in this way the infiltration of water and

humidity in the cable. [15, pg 36]

The armoring should support the tensional forces (the own weight of the cable and the

dynamic forces caused by the movements of the vessel) and presents enough

mechanical resistance to external aggression (installation tools) during the cable

installation. Hence, the armoring provides tension stability and mechanical protection.

[15, pg 48]

The outer armour of the cable consists of approximately 105 round galvanized steel

wires, each one having a cross section of 5.6 mm2. The submarine cable system

includes also a fibre optic cable which allows the communication between the turbines

the accommodation platform and the shore. The external layer consists of two layers

of polypropylene yarn and bitumen. [31]

2.2.2 Land Cable

The land cable consists in two sections. One section with 2.3 km joining the

submarine cable with Blaabjerg station and another cable section from Blaabjerg with

55.4 km to Endrup station.

These cables are three single phase conductor aluminium cables produced by ABB with

a cross section of the conductor of 1200 mm2. The voltage rating is 150 kV. These

cables are laying in flat formation.

One semiconducting layer is introduced to fill the gaps between the conductor and

insulation material and to ensure a radial electric field distribution. XLPE is used as a

dielectric in the cable with a layer thickness of 17 mm.

The screen is formed by copper wires, each one having a diameter of 1.1 mm and a

total cross section of 95 mm2. An aluminium sheath of 0.2 mm is used in order to

prevent moisture and water from the penetrating cable. The external sheath consists

of a 4.0 mm PE layer.

The complete cable presents a diameter of 27 mm and a weight of 9 kg/m.

13

Fig.2.5 Layout of the single conductor land cable [22]

The three phase cable is buried at 1.3 m below the land as is shown in the next figure:

Fig. 2.6 Laying of the 150 kV land cable

Data of the land cable.

Parameter Unit Value

Conductor Outer radius

Material

mm

-

20.75

Aluminium

Conductor screen Thickness

Outer radius

mm

mm

1.5

22.25

Thickness mm 17

14

Dielectric Outer radius

Material

mm

-

39.5

XLPE

Dielectric screen +

swelling tape

Thickness

Average outer radius

mm

mm

1.6

41.1

Metallic sheath

Thickness

Average outer radius

Material

Cross section

mm

mm

-

mm2

1.11

42.21

Copper

95

Water barrier

longitudinal

Thickness

Average outer radius

mm

mm

0.6

42.81

Water barrier radial Thickness

Average outer radius

mm

mm

0.2

43.01

Outer covering

Thickness

Average outer radius

Material

mm

mm

-

4

47.5

PE

Table 2.2 Land cable data [22]

2.3 Grounding of the cable

The sheath is metallic and performs different functions like prevent moisture

ingress into the insulation, contains cable pressure in fluid-filled cables, provide a

continuous circuit for short-circuit fault current return and prevent mechanical

damage. The three phase cables may be laid close to each other. As there is ac current

flowing in the core of one cable, as well as currents flowing in adjacent cores, induced

voltages on the metallic sheath(s) of the cable(s) appears. In order to limit these

voltages and prevent cable damage, the conducting sheaths are grounded using

different methods.

Grounding method Voltage at cable end Sheath voltage

limiter(surge

arrester)

Typical application

Single end Yes Yes Usually not used for

HV cables

Both end No No Short cables

Cross bonding At cross bonding points Yes Long cables where

joints are required

Table 2.3 Grounding methods for cables. [13]

The sheaths of the two land cables are cross bonded in order to reduce the cable

losses. This method is used for long cables where shunt reactors and joints are

required. The cable is sectionalized in one or more major sections. Each of these major

sections is formed by three minor sections of equal length. [40]

This method minimizes the total induced voltages in the sheath in order to minimize

the circulating currents and the losses. The best configuration is achieved when the

15

cores of the three minor sections within each major section are perfectly transposed

but the sheaths are not. This is shown in the figure 2.7.

At both ends of the major sections, the sheaths are solidly bonded and earthed.

Nevertheless, at the minor sections, they are bonded to sheath voltage limiters.

Earthing both ends of each major section eliminates the necessity of an earth

continuity conductor. [42]

Under positive phase sequence conditions (PPS) and due to the cores are perfectly

transposed, the resulting voltages in each minor section are separated by 120 degrees,

summing zero. Thus, no sheath currents will flow. If cross bonding only the sheaths

but not the cores, a good balance is not achieved unless the cables are laid in trefoil

configuration. Therefore, the cores of cross-bonded cables laid in flat formations are

generally transposed. [46, pg 145]

Fig. 2.7 Cross bonding method with transposition of the cores [46, pg 144]

A change in the sheaths at the cross-boning points represents an electrical

discontinuity. Therefore, travelling waves will be reflected, and relatively high transient

sheath overvoltages will occur at the cross bonding points. Metal oxide surge arresters

or metal oxide varistors (MOVs) could be used to eliminate its influence. [40]

16

Fig. 2.8 Layout of a cross-bonding cable system [31]

The total length of the cable sheath, 55.4 km, is cross bonded using 11 major sections,

being the length of the individual sections between 587 m to 1846 m. [map of the

cable, energinet.dk]

During the study of the 2.3 km cable was found out that it has a special configuration

owing to its sheath is cross bonding at points B and D but not at junction C. The minor

section between B and D is formed by two sections connected by an ideal conductor in

point C.

Fig. 2.9 Special cross bonding at the 2.3 km cable. [22, pg 13]

2.4 Connection of the sub-systems

The connection to land consists of three main sub-systems: transformer

platform, a submarine cable and a land cable. The total length of the cable is just less

than 100 km long. A 42 km long submarine cable is connected to a 2.3 km land cable

and this cable is connected to the 80 MVAr reactor at Blaabjerg station. The 2.3 km

land cable is joint with another 55.4 km land cable to reach Endrup 400/150 kV

transformer station.

17

Fig. 2.10 Global scheme of the system. [5]

As mentioned in the introduction the shunt reactors are used to compensate the

reactive power produced by the capacitance of the cables.

Two reactors are presents at Endrup station, of 40 MVAr and 80 MVAr respectively. A

third reactor of 80 MVAr is installed between the 2.3 km and 55.4 km land cable a

Blaabjerg station.

The 80 MVAr reactors at Blaabjerg and Endrup are of the same type. Hence, the

system has a compensation factor of 100% since the reactive power production of the

combined cable network is approximately 200MVAr [22].

The shunt reactor data is given below.

40 MVAr Endrup 80 MVAr Endrup 80 MVAr Blaabjerg

Rated voltage 170 kV 170 kV 170 kV

Rated power 40 MVAr 80 MVAr 80 MVAr

Table 2.4 Shunt reactor data

In order to connect the wind farm with the 400 kV grid, three different transformers

are used. For each turbine a 2.6 MVA transformer is installed. Their main

characteristics are listed below.

Auto-transformer Wind farm

transformer

Turbine

transformer

Rated voltage 410/167.6 kV 165/35/35 kV 34/0.69 kV

Rated power 400 MVA 220 MVA 2.6 MVA

Vector group YNyna YNd11d11 dYN11

Table 2.5 Transformers data.

The main 400/150 kV autotransformer supplies station Endrup from Kassø. The wind

farm transformer is a three winding transformer with a power rating of 220MVA.

18

3. Problem analysis

In this chapter will be described the origin of the phenomena associated during the

energization of a cable.

Introduction

The voltages stresses of the system arise from different overvoltages. These can

be external like lightning discharges, or internal like: switching operations, faults on

the system or load fluctuations. Switching overvoltages are dependent on the rated

voltages, the time at which the change in the operating voltage occurs, etc… *34+

The main operations that can produce switching overvoltages are line energization and

de-energization, capacitor and reactor switching, presence of faults and circuit breaker

openings. [9]

Switching operations are regarded as a transient phenomenon that occurs in the

power system when the network changes suddenly from one state into another. This

transient period is very small compared with the time spend in steady state condition.

Despite this, it has great importance, the largest stresses caused by overvoltages or

overcurrents arise at this period. At extremely cases can cause damages like disable a

machine or shut down a plant, depending on the circuit involved. [32]

An accurate estimation of the switching overvoltages is an important factor in the

design of the transmission system, which can have a significant influence on its cost.

The design of the insulation level required by the equipment is based on these

switching overvoltages. [32]

3.1 Cable Models

In electromagnetic transient simulations there are basically two ways to

represent transmission lines: PI sections or using distributed transmission lines.

Distributed models are based on the principle of the travelling waves and are more

suited for transient studies.

3.1.1 PI Section model

This model cannot accurately represent other frequencies that differ from the fundamental one, unless many sections are used. The using of many sections is inefficient due to increase the computational time. Also, it cannot represent frequency dependent parameters of a line, such as skin effect. [25]

19

3.1.2 Distributed models

They take into account the distributed nature of the cable parameters. Can be

differenced the models: Bergeron’s, the frequency dependent (mode) and the

frequency dependent (phase).

The Bergeron model

This model represents the resistance in a lumped manner, for example: 1

2 in the

middle of the line and 1

4 at both ends. The inductance and capacitance however, are

considered distributed along the line. According to [25] this model is suitable for load

flow analysis.

Frequency dependent (phase/mode):

The frequency dependent models are used for a precise modeling and for the studies

where the signal presents more frequencies than the fundamental (particularly for

transient studies). Both are distributed parameter models and all parameters are

frequency dependent. Because of this they are superior to both π-models and the

Bergeron model. [38]

EMTP (Electromagnetic Transients Program) is the most widely used tool for the

analysis of electromagnetic transients in power systems. The differential equations

that describe the behavior of the n-conductors of cable system are separated in n

different equations.

In the frequency-domain, the sets of second-order differential equations in general

form of a multi-conductor transmission line or underground cable.

2

2

d VZYV

dx (3.1)

2

2

d IYZV

dx (3.2)

Where Z and Y are the series impedance and shunt admittance matrices per-unit

length, respectively. For an n conductor system they are n × n matrices. [41] The

coefficient matrices ZY and YZ are full matrices (there are not zero terms). Hence,

there are couplings among the individual voltage equations in (3.1). Also there are

couplings among the individual current equations in the set in (3.2). Hence, the

transmission lines consist of several mutually coupled phases that need to be broken-

up into modes. So, the resulting system of n differential equations is solved through a

modal analysis.

20

For example, single core cable presents three different modes of propagation: coaxial

mode, inter-sheath mode and ground mode.

Coaxial mode concerns to the current in core conductor that fully returns in the screen

of the same cable and no net current flows in the ground. Inter-sheath mode when

the current in screen conductor fully returns in one or both of the other screens and

no net current flows in any of the core conductors. Meanwhile, ground mode refers

when current in the three screens fully returns through the ground and no net current

flows in any of the cores. [47]

In modal analysis the response of the system is calculated individually for each mode

and the total solution is obtained by the summation of the individual results.

Once obtained the modal results, it can be obtained the phase results through a

transformation as shows the next equation.

·tmode phaseV Q V (3.3)

1·mode phaseI Q I (3.4)

Where Q is the modal transformation matrix. [48] Between the two frequency dependent models, the frequency dependent phase

model (FDP) is most accurate than the FDM (frequency dependent mode). This is

because in FDM, Q is considered constant; while in FDP matrix Q is frequency

dependent. Because of this frequency dependent the model is able to reproduce high

and low frequency phenomena in the same simulation. [48]

The representation of the Horns Rev II cable is done by a frequency dependent phase

model, due to it is numerically robust and more accurate than any other available

models. [25]

3.2 Problems associated during the energization of the cable

Based on the results obtained in the paper [5], the following transient

behaviors are explained during cable energization.

3.2.1 Closing of the circuit breaker

The closing of the circuit breaker is synchronized closed at zero voltage. A large

transient occurs when the cable is being energized when one of the three phase

voltages is at its peak at the instant of switching. On the other hand, the lowest voltage

occurs if the circuit breaker switches on the three phases individually when the phase

21

voltage is crossing zero. In order to explain the overvoltage a simplified single-phase

model of a cable is represented by a lumped LC circuit. [13]

C

VinVc

IL

SL

Fig. 3.1 LC series circuit.

Fig.3.2 Results of the energization on an LC circuit. Blue: voltage at the source. Green:

voltage at the capacitor. Red: current through the inductor.

In the simulation the switching occurs when the source voltage is at its peak value.

From the instant of switching, the capacitor is charged by the current, which is flowing

through the inductance. The transient is then, initiated with the system natural

frequency:

02

km km

1f

2π L C l (3.1)

After a short moment the voltage across the capacitor is the same as the source,

reaching the current its peak value. By energy conservation the current in the inductor

cannot change rapidly. Thus, the capacitor voltage continues increasing until the

current crosses zero. At this moment the capacitor reaches its peak value and begins

to discharge. The system was considered lossless, the transient is not damped. A real

cable has some resistance which damps the oscillations. As the source is sinusoidal Vc

22

will match the source voltage at different points for the system natural frequency in

each cycle. Therefore, the amplitude of Vc will change for each cycle. [13]

The comparison voltage in the sending end between the measurements (Vendrup) and

the simulation results presents an error of 1.5%. This is shown in the figures 3.5 and Fig.

3.6.

Fig. 3.3 Measured sending end voltage.

Fig 3.4 Simulated sending end voltage during energization.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-200

-150

-100

-50

0

50

100

150

200Sending end voltage - measurement

Time [s]

Voltage [ k

V ]

Phase a

Phase b

Phase c

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-150

-100

-50

0

50

100

150

Sending end voltage - PSCAD

Time [s]

Voltage [ k

V ]

Phase a

Phase b

Phase c

23

3.2.2 Influence of the shunt reactor on the cable

High Voltage AC cables are characterized by a large capacitance. Therefore, when connecting a load, a capacitive charging current per phase (Ic) will flow through the cable. The capacitance and charging current increases linearly with the cable length, limiting the cable capability for carrying current without showing deterioration, like overheating.[42] The charging current is defined with the following formula:

cI UC l (3.2)

This equation can also be expressed as:

c rI U l (3.3)

Where l the length of the cable, ω is is the angular frequency, rε the relative

permittivity of the insulation and U is the phase voltage. The length of the cable is

dependent on the charging current. For full critical length only charging current is

transmitted. No active power is transmitted without overheating the cable. It is also

noticed, that the critical length is reduced, either increasing the phase voltage or the

permittivity of the insulation. Shunt reactors are connected in parallel to the cable, in

order to compensate for both the reactive power generated by the line and the

reduction of transmitted active power. This compensation will lower the voltage

decreasing the charging current. [42]

The reactive power consumed by the shunt reactor is defined by the formula:

2

ω

UQ

L (3.4)

Where L is the inductance of the shunt reactor. Decreasing the value of the inductor,

will increase the reactive power compensated. The voltage will be lower if the reactive

power absorbed increase. A correct placement of the shunt reactors can decrease

Ferranti effect.

As the drop voltage is not equal along the cable, the amount of reactive power

consumed will change as a function of the position. The compensation level and

location must be carefully designed. In the next figure is illustrated the loading of an

open ended line due to the charging current for different schemes of compensation

level and placement.

24

Fig.3.5 Capacitive charging current depending on the placement and level of

compensation. [42]

It is observed that the worst case occurs when the compensation is only located at one

end. A better solution is to install the compensation in the middle of the line. In this

way the reactive current will flow through the reactor from both sides and therefore,

only half of the charging current will flow through the most loaded points. This

situation is also achieved if the compensation is equally distributed at both ends. The

configurations, either in the middle of the line or near the receiving end are the

preferred ones.

In the next figure, Fig.3.6, it is shown the comparison between one phase current in

the shunt reactor with the simulation results. This figure shows a good agreement with

almost no difference between them.

25

Fig.3.6 Comparison shunt reactor current in phase b).

Zero missing phenomenon

Shunt reactors are connected in parallel to the cable, in order to compensate the

reactive power generated by the line and in this way avoid the reduction of

transmitted active power. This configuration produces resonant behavior between the

capacitance of the cable and the inductance of the shunt reactor. [13]

It is possible to represent the shunt reactor as an inductor and the cable as a capacitor

considering that the resistance of the shunt reactor is very small in comparison with its

inductance. [12]

L C

VinVc

IL

S

IBRK

IC

Fig.3.7 L-C parallel circuit.

The AC current flowing through the cable will be ideally 900 leading the voltage. The

opposite will occur with the current flowing through the shunt reactor (900 lagging).

They cancel out each other and the shunt reactor compensates the reactive power

generated by the cable. [13]

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2Phase b

Time [s]

Curr

ent [ kA

]

Measurement

PSCAD

26

The transient reactor’s current also presents a DC component, which is difficult to

damp because of the low losses. The resistance of the system formed by the three

cables and the shunt reactor is small.

The damping of the DC component can take several seconds. During those seconds the

current does not cross zero, the circuit breaker cannot be open without risk of damage,

unless it is designed to interrupt DC currents or currents with several amperes.

There are 900 of difference between voltage and current in the inductor, thus, if the

circuit breaker is closed at zero voltage the current should be at its peak value. It is also

known that the current in an inductor must keep its continuity, without changing

rapidly. Assuming that the current in the inductor is equals to zero before the

connection moment, it must be zero after the connection. Therefore, if the inductor is

not connected for a peak voltage, to maintain its continuity the DC component takes a

negative value of the AC component in the connection moment. If the inductor is

connected for a peak voltage no DC component is present. This method is called

synchronous closing. [12]

Fig.3.8 Representation of the current in the inductor (dashed line), the current in the

capacitor (dotted line) and resulting DC component.

If there is no resistance in the system, the DC component is not damped and it will be

maintained infinitely. In reality there is always some resistance and the DC component

disappears after some time. [12]

Connecting at the voltage peak, the current should be zero. Due to the difference

between the phases, voltage and current is 900. On the other hand, if connecting when

the voltage is zero, current should have a peak value.

The energization of the Horns Rev II cable is performed using synchronized switching at

zero voltage. The DC component in the shunt reactor installed in the middle of the line

is close to its peak. The comparison between measurements and simulations carried

out in [5] shows that:

27

The DC component is damped faster in the real system than in the simulated

one.

Fig.3.9 Current measured in the shunt reactor.

Fig. 3.10 Shunt reactor simulated current.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-1.5

-1

-0.5

0

0.5

1

1.5Current - Shunt reactor - measurement

Time [s]

Curr

ent [ kA

]

Phase a

Phase b

Phase c

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Current - Shunt reactor-PSCAD

Time [s]

Curr

ent [ kA

]

Phase a

Phase b

Phase c

28

For the sending end the current peak values are slightly smaller in the

simulation.

Fig.3.11 Sending end measured current. Phase c) it is not shown due to it was not

measured.

Fig. 3.12 Sending end simulated current. Phase c) it is not shown due to it was not

measured.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-1.5

-1

-0.5

0

0.5

Sending end current - measurement

Time [s]

Curr

ent [ kA

]

Phase a

Phase b

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-1.5

-1

-0.5

0

0.5Sending end current - PSCAD

Time [s]

Curr

ent [k

A]

Phase a

Phase b

29

3.3. Problems in Steady- State

Ferranti effect

During energization the circuit breaker in the receiving end is left open. Because of the

charging current of the cable’s capacitance, a negative voltage drop across the cable

may occur. This means that the voltage at the receiving end will be higher than the

sending end. This phenomenon is called Ferranti Effect and can be explained using the

nominal π model, shown in the next figure. [21]

Ur

R

Us C1 C2

L

Fig. 3.13 Pi model of the cable regardless the shunt reactor.

The voltage in the receiving end can be found on basis of fig. 3.10. The capacitance in

the sending end has no influence on the voltage drop along the cable. rU is defined as:

2

2

2

2C

r s s

C series

jZ CU U U

Z Zj j L

C

(3.5)

Reorganazing this equation we can isolate Ur as:

212

s

r C

UU

L

(3.6)

Where L is the cable’s inductance, C2 is the cable’s capacitance, Us sending voltage, Ur

the receiving voltage and l is the cable’s length.

The length of Horns Rev 2 is 99.7 km and is open ended during the measurements, so

an increase in the receiving voltage is expected. This increase would be higher if no

shunt reactor is connected on the line.

From [5] it is known that the measurements show an increase in the voltage of the 8%.

This is shown in the Fig. 3.16:

30

Fig. 3.14 Measured voltages in the sending and receiving end.

In the next figure it is shown the difference between the simulated voltage in the

sending end and the simulated voltage in the receiving end.

Fig. 3.15 Difference between the voltage in the sending end and receiving end.

In Fig 3.16, a wider view of Fig 3.15 is shown. In this figure can be observed that the

simulations shown an unexpected result. There is almost no Ferranti Effect, 1.7% of

increase on the voltage.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-200

-150

-100

-50

0

50

100

150

200Comparison - Sending end - Receiving end - Measurement

Time [s]

Voltage [ k

V ]

Sending

Receiving

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-150

-100

-50

0

50

100

150

Comparison - Sending end - Receiving end - PSCAD

Time [s]

Voltage [ k

V ]

Sending

Receiving

31

Fig. 3.16 Wider view of the figure 3.15.

The voltage comparison in the receiving end for phase a) is shown in the figure 3.17. In

this figure the difference between the simulation and the measurement is noticed and

estimated to be 4.7%. [5]

Fig. 3.17 Voltage comparison between measurement and simulation at the receiving

end.

0.18 0.181 0.182 0.183 0.184 0.185 0.186 0.187 0.188 0.189 0.190

20

40

60

80

100

120

140Comparison - Sending end - Receiving end - PSCAD

Time [s]

Voltage [ k

V ]

Sending

Receiving

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-150

-100

-50

0

50

100

150

Phase b

Time [s]

Voltage [ k

V ]

Measurement

PSCAD

32

Conclusion

The conclusions from the comparisons named before are explained using the figure

3.19, where A, B and C are the measurement points.

Vgrid CB1

Zgrid

Endrup

Horns Rev II

land cable

55.4 km

land cable

2.3 km

sea cable

42 km

150 kV400 kV

A CB

80 MVar

Blaabjerg

B’

Fig. 3.18 Representation of the measurement points in the system.

Through the voltage comparison in the sending end of the line (fig. 3.3 ,fig. 3.4)

and the one for the currents in the shunt reactor (fig. 3.6 ) is proved the accuracy of

the 52 km land cable model (from point A to point B). This fact also proves the validity

of the 2.3 km land cable model, due to both are modeled in the same manner. In this

way it is concluded that the model is correct until the point B’. The disagreement in

point C (Fig. 3.18) can only be caused by the submarine cable. Therefore, an

improvement in its model is needed.

3.4 Effect of the cable on the grid

The cable was open ended during the energization and due to it is mainly a

capacitive element, an increase in the busbar voltage was expected. This behavior was

already explained in the point 3.2.1.

Fig. 3.19 Measurement of the onshore voltage during cable connection.

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

-150

-100

-50

0

50

100

150

Sending end voltage-Connection

Voltage[k

V]

Time [s]

Phase a

Phase b

Phase c

33

Fig. 3.20 Simulated Sending end voltage.

The voltage at both sides of the circuit breaker was measured in order to see this

effect. The measurements carried out in [5] shown that there is a permanent increase

of the voltage in the busbar of approximately 6%. In the simulation the increase of the

voltage is smaller, approximately 4.6%.

3.5 Problem statement

During energization transient voltages and currents can reach high values,

therefore, the components of the system can be damaged. The overvoltages can also

propagate to lower voltage levels, where they may cause a breakdown of electronic

equipment.

In order to design the appropriate protection for the components against these

transients it is necessary to achieve knowledge about the transient phenomena in the

cable system.

The main problems explained before can be resumed as follows:

The steady-state measurements shows a large Ferranti Effect, the voltage is 8%

higher in the end of the line, while the simulation results only present 1.7%.

The simulations were in accordance with the expected results but not with the

measurements at the receiving end during steady-state.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

-150

-100

-50

0

50

100

150

Time[s]

Voltage[ kV

]

Sending end simulated voltage

Phase c

Phase b

Phase a

34

Effects like the capacitance between phases and between the phases and the outer

amour have to be included in the model of the submarine cable. Otherwise the lack of

detail can lead to wrong results when performed simulations on long HVAC. [5]

3.6 Aim of the project

The work carried out during the project period is based on a case study of a 100

km cable installed by Energinet.dk in 2009, between the offshore wind farm Horns Rev

2 and the onshore Endrup substation.

The aim of the report is summarized in the following:

Compare the measurement results carried out in a preliminary report with the

simulations done in PSCAD.

Explain why the submarine cable model is inaccurate.

Improve the submarine cable model

3.7 Solution method

In order to investigate the transient phenomena during the energization of a

line consisting of underground cable, sea cable and shunt reactor, a suitable model is

built in PSCAD.

3.8 Limitations

The limitations encountered when performing the project report are listed below:

- PSCAD software does not allow the modeling of a three core cable surrounded

with a common armor (pipe-type cable). - The license available in PSCAD does not allow the representation of the whole

system, (some simplifications were performed, for instance the number of

cross bonding points of the 52 Km land cable). Therefore, only the part of the

system described is built and simulated.

35

4. Comparison between theory equations and PSCAD results

In this chapter the current submarine cable model used in PSCAD is explained

and analysed, based on its defining equations.

4.1 Submarine cable model in PSCAD

The figure below shows the PSCAD implementation of the three single

conductor cables in close triangle.

Fig.4.1 Layout submarine cable

The characteristic parameters of the submarine cable model are calculated as is

explained below:

Core

It is not possible to model segmented conductors in PSCAD and in this case the

conductor is stranded with copper wires. Therefore, the resistivity needs to be

increased using the next approximation:

2

1c c

c

r

A

(4.1)

Where c is the increased resistivity, c is the resistivity of the copper core, cA is the

(nominal) cross sectional area of the core and r1 is the radius of the core. [45]

100.0 [ohm*m]

Relative Ground Permeability:

Ground Resistivity:

1.0

Earth Return Formula: Analytical Approximation

15.25 [mm]

Cable # 1

37.75 [mm]40.15 [mm]42.45 [mm]

1.3 [m]

0 [m]

Conductor

Insulator 1

Sheath

Insulator 2

15.25 [mm]

Cable # 2

37.75 [mm]40.15 [mm]42.45 [mm]

1.37352 [m]

-42.4505 [mm]

Conductor

Insulator 1

Sheath

Insulator 2

15.25 [mm]

Cable # 3

37.75 [mm]40.15 [mm]42.45 [mm]

1.37352 [m]

42.4505 [mm]

Conductor

Insulator 1

Sheath

Insulator 2

36

Insulation and semiconductive layers

There is not possible to model the semiconductive layers directly. Their influence

needs to be included when modelling the insulation system. Basically, the diameter of

the insulation is increased to include these semiconducting layers and the permittivity

it is modified as follows:

2

1'

i

rln

r

bln

a

(4.2)

Where i is the relative permittivity of the insulation, r2 and r1 are the inner radius of

the sheath and the outer radius of the conductor respectively; a and b are the inner

and outer radius of the insulation. [47]

The phase sheath was modelled as 2.4 mm thick solid layer. Using (4.1) the resistivity is

found to be 22·10-7 Ω·m. The most outer layer of the single conductor is a

semiconducting layer. As this layer cannot be implemented in PSCAD, it was

approximated as an insulating layer with a permittivity of 1000.

1st Conducting layer Outer radius Resistivity Relative permeability

15.25 mm 1.99·10-8 Ω·m 1

1st Insulation layer Outer radius Relative permittivity Relative permeability

37.75 mm 2.857 1

2nd Conducting layer Outer radius Resistivity Relative permeability

40.15 mm 2.2·10-8 Ω·m 1

2nd Insulation layer Outer radius Relative permittivity Relative permeability

42.45 mm 1000 1

Table 4.1 Data of the submarine cable used in the PSCAD model. [22]

The main difference between the submarine cable of Horns Rev 2 and the SC modelled

in the simulations is the lack of a common armor surrounding the three conductors

disposed in touching trefoil configuration. Because of the consequences that this

simplification may have caused, an important issue is to study the voltage results at

the receiving end of the cable in the two configuration types.

The simplified model that is shown below (fig.4.2), composed by an ideal voltage

source and the sea cable, is used to get the voltage results from the simulation at the

receiving end.

37

Fig. 4.2 42km Submarine cable modelled in PSCAD.

4.2 Receiving end voltage of each configuration

As it was explained before, a three-core cable in touching trefoil is the

disposition used in the model of the simulations, while the SC of Horns Rev 2 consists

in a pipe type-cable. As it is shown the figure below, the difference between the two

configurations is the common armor surrounding the conductors.

Fig 4.3 Pipe-Type Cable (a) and three phase cable in touching trefoil (b). [46]

In this chapter is described the method followed to verify the results of the simulations

from the current model and the future improved model for the SC. This method

38

consists in compare the voltage at the receiving end (Vreceiving) of the simulations with

the one calculated through the equations from [39] and [54].

In order to calculate Vreceiving is necessary to solve this system of equations:

· · · receiving c receiving c sending sendingI Y V H Y V I (4.3)

· · ·sending c sending c receiving receivingI Y V H Y V I (4.4)

The characteristic admittance, Yc can be obtained through the impedance (Z) and the

susceptance (Y) matrix of the SC from as:

1( ) ( ( )· ( )) · ( )Yc Y Z Y (4.5)

The propagation matrix, H is calculated from the following expression [54], where l is

the total length of the submarine cable (42 Km).

· ·· l Y ZlH e e

(4.6)

The current Ireceiving is zero due to the line is open at the receiving end. Applying this

condition in the equations (4.3) and (4.4), the resulting expressions are:

0 · ·c receiving c sending sendingY V H Y V I (4.7)

· · ·sending c sending c receivingI Y V H Y V (4.8)

Hence, solving this system of equations both voltage at the receiving end and current

in the sending end can be obtained.

In the subchapter 4.2.1 (three-core in touching trefoil) is presented the Vreceiving

comparison between the simulations and the results obtained using the equations

mentioned before, in order to check the accuracy of the current PSCAD model.

In the subchapter 4.2.2 (pipe-type cable) it is calculated the expected voltage at the

receiving end for the submarine cable, using the same equations as before. This result

will be compared with the new model in PSCAD.

39

4.2.1 Three –Core in touching trefoil

In the touching trefoil configuration the sheaths (Si) are connected to ground

(see fig. 4.3). Therefore, all the susceptances and impedances named below are

referenced to ground.

Impedance matrix

The matrix Z represents the own impedances of the core conductors and the sheath

and the mutual impedances between the core and the sheath, which exist due to the

electromagnetic coupling [46, pg. 149]. The relationship between voltage and currents

for a three core cable in touching trefoil configuration is defined as follows:

1 1

1 1

2 2

2 2

3 3

3 3

1

1

2

2

3

3

C C

S S

C C

S S

C C

S S

V IC e b b a b b

V IS b e b b a b

V IC b b e b b a

V IS a b b f b b

V IC b a b b f b

V IS b b a b b f

(4.9)

Using the equations defined in [46, pg. 156], which are developed in the appendix, and

having into account the relationship between the terms disposed in the previous

matrix, the impedance matrix is now defined as:

*Ω/m+

8.9e-5 + 7.1e-4i 4.9e-5 + 6.3e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i

4.9e-5 + 6.3e-4i 3.3e-3 + 6.3e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i

4.9e-Z

5 + 5.8e-4i 4.9e-5 + 5.8e-4i 8.9e-5 + 7.1e-4i 4.9e-5 + 6.3e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i

4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 6.3e-4i 3.3e-3 + 6.3e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i

4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 8.9e-5 + 7.1e-4i 4.9e-5 + 6.3e-4i

4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 6.3e-4i 3.3e-3 + 6.3e-4i

40

Susceptance matrix

The susceptance matrix, Y represents the own susceptances of the core conductors

and the sheath. The own susceptance of the core is the same as the one between the

core and the sheath, as they are connected to ground.

Below is showed the susceptance matrix Y, which terms are calculated as [46, pg. 146]

in the appendix.

[S/m]

Voltage comparison

Solving the system equation (4.7 and 4.8), Vreceiving and Isending can be calculated through

the following expressions:

1

· 2· · · · · · · ·sending c sending c c c c sendingI Y V H Y Y H H Y H Y V

(4.10)

1

2· · · · · ·receiving c c c sendingV Y H H Y H Y V

(4.11)

Whereas:

1 1

1

2 2

2

3 3

3

0

0

0

C C

S

C C

sending

S

C C

S

V V

V

V VV

V

V V

V

(4.12)

Vsending is zero in the sheaths because they are grounded.

5.51e-8i -5.51e-8i 0i 0i 0i 0i

-5.51e-8i 3.14e-4i 0i 0i 0i 0i

0i 0i 5.51e-8i -5.51e-8i 0i 0i

0i 0i -5.51e-8i 3.14e-4i 0i 0i

0i 0i 0i 0i 5.51e-8i -5.51e-8i

0i 0i 0i 0i -5.51e-8i 3.14e-4i

Y

41

The figure below shows the voltage comparison in the receiving end of the line for the

core conductor of the phase a).

Fig. 4.4 Comparison between equations and simulations results for the Vreceiving in the

phase a.

Due to the Vreceiving comparison from the simulations and the one calculated through

the equations presents an error of 0.62%, it is concluded the validity of the simulations

results and the method proposed.

4.2.2 Pipe type cable.

The submarine cable is considered as a pipe type cable with three conductors in

touching formation, where the pipe is made out of steel wires. The armor acts as a

third conductor in addition to the core and the sheath.

Fig. 4.5 Cross-section of the submarine cable.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-150

-100

-50

0

50

100

150Voltage receiving end

Time [s]

Voltage [kV

]

equations

simulations

42

Impedance matrix

To calculate the Z matrix the equations from the previous section are used again,

adding the self- impedance of the amour Zaa. The relationship between voltage and

currents for three core armoured cable configuration is defined as follows:

1 1

1 1

2 2

2 2

3 3

3 3

C C

S S

C C

S S

C C

S S

A A

e a b b b b c

a f b b b b c

b b e a b b c

b b a f b b c

b b b b e a c

b b b b e a c

V I

V I

V I

V I

V I

V I

c c c c c c dV I

(4.13)

Although Z matrix terms are calculated in the appendix, the own impedance of the

armour is presented below in order to explain how affects µa (permeability of the

armor) in its calculation. The self- impedance of the amour including earth return is

given by:

2 4 4

10 4 10 ,

4

a ercaa oa ia ea ac

oa

DZ R f j f xf r r log

r km

(4.14)

Whereas, a ac

R is the ac resistance, f is the operation frequency (50 Hz) ,oa iar r are

the outer and the inner radius of the armour respectively and ercD is the depth of the

earth return conductor. The ac resistance and the depth of the earth return conductor

are developed in the appendix.

As it is explained in [7], the permeability of a wired steel amour, µa , depends on the

wire diameter, the laying angle and the intensity of the circumferential magnetic field.

The normal values for the permeability are chosen to be, either µa = 1, or µa = 10.

The self impedance of the amour for both cases, are presented below:

µa=1 6.096 004 5.8348 004 /aaZ e e i m

µa=10 6.096 004 6.8858 004 /aaZ e e i m

Table 4.2 Values of the self- impedance of the amour.

As it is shown above, the relative permeability does not affect strongly the result of the

self impedance of the armor. Therefore, below is presented Z matrix calculated with

µa=1.

43

*Ω/m+

Susceptance matrix

The capacitances presented between the different layers of the SC are discussed doing

a finite element study (QuickField software) on a section of the cable.

The characteristics of each layer are taken from table 2.1. Both XLPE insulation and the

semiconducting layer of polyethylene has a permittivity of Ɛ=2.875. Figure below

shows the boundary conditions imposed in the problem.

Fig. 4.6 Boundary conditions for the finite element study

Although, the cable is bonded in both ends, small voltages can appear through the

sheath, caused by the skin effect. This phenomenon appears at high frequencies,

9.9e-5 + 7.1e-4i 4.9e-5 + 6.3e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 1.7e-4i

4.9e-5 + 6.3e-4i 3.3e-3 + 6.3e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-

z

5 + 5.8e-4i 4.9e-5 + 1.7e-4i

4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 9.9e-5 + 7.1e-4i 4.9e-5 + 6.3e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 1.7e-4i

4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 6.3e-4i 3.3e-3 + 6.3e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 1.7e-4i

4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 9.9e-5 + 7.1e-4i 4.9e-5 + 6.3e-4i 4.9e-5 + 1.7e-4i

4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 5.8e-4i 4.9e-5 + 6.3e-4i 3.3e-3 + 6.3e-4i 4.9e-5 + 1.7e-4i

4.9e-5 + 1.7e-4i 4.9e-5 + 1.7e-4i 4.9e-5 + 1.7e-4i 4.9e-5 + 1.7e-4i 4.9e-5 + 1.7e-4i 4.9e-5 + 1.7e-4i 6.1e-4 + 5.8e-4i

44

where alternating currents tend to avoid to be conducted along the centre of a solid

conductor, locating its conduction near the surface.

In this report it is considered the analysis of the submarine cable during steady state

conditions for a frequency of 50 Hz. Therefore, the voltages both in the armour and in

the screen are considered to be zero all along the 42 km of SC. Thus, both the armour

and the three sheaths are connected to ground through their outer surface, imposing a

0 V boundary condition in the outer radius of each one.

As the skin effect is neglected, a homogenous current distribution in the core can be

considered. Therefore, the voltage boundary condition is set up in the inner radius of

the insulation.

The capacitance between two surfaces is obtained through the storage energy

between the layers and the potential difference as:

2 2 2

1 2

1 1· · ( )

2 2W E dV C V V (4.15)

The voltage boundary condition must be an instantaneous value of the nominal

voltage (159 kV). Taking the maximum Va (t= 0), as a possible value, the voltage

condition imposed is:

2 2

159· ·cos 2· · · 0 1 59· 1 29.82 3 3

Va f t kV kV kV (4.16)

2 2

159· ·cos 2· · · 120 1 59· ·cos 120 64.911 3 3

Vb f t kV kV kV (4.17)

2 2

159· ·cos 2· · · 120 159· ·cos 120 64.911 3 3

Vc f t kV kV kV (4.18)

The voltage distribution on the section of the cable once the model is meshed and

solved is presented in fig. 4.7.

45

Fig. 4.7 Voltage distribution on a cross section of the cable

Only if two layers present different potential the capacitance will be took into account,

as is shown in equation (4.14). Taking into account the simplification named before,

(the voltages on the sheaths and on the amour are 0 all along the SC) Fig. 4.7 proves

that the capacitance between sheath and armor and sheath-sheath, are not

considered because their layers present equal voltages.

As a resume, it can be said that the capacitances between bonded layers are not

considered in the susceptance matrix of the cable. The electrical scheme that

represents the capacitances between the different layers on a section of the cable is

shown in fig. 4.8.

46

C1 C3S3

S2S1 C2

A

Fig. 4.8 Electrical scheme of the cable (all the capacitors have a value equal to Ccs).

The susceptance matrix Y, is shown below and its terms are described in the appendix.

[S/m]

4.43 7 5.54 8 1.11 7 5.54 8 1.11 7 5.54 8 5.54 8

5.54 8 3.14 4 5.54 8 0 5.54 8 0 0

1.11 7 5.54 8 4.43 7 5.54 8 1.11 7 5.54 8 5.54 8

5.54 8 0 5.54 8 3.14 4 5.54 8

e i e i e i e i e i e i e i

e i e i e i e i

e i e i e i e i e i e i e i

e i e i e i e iY

0 0

1.11 7 5.54 8 1.11 7 5.54 8 4.43 7 5.54 8 5.54 8

5.54 8 0 5.54 8 0 5.54 8 3.14 4 0

5.54 8 0 5.54 8 0 5.54 8 0 1.49 7

e i e i e i e i e i e i e i

e i e i e i e i

e i e i e i e i

47

Voltage results

As in the touching trefoil configuration, the voltage in the receiving end can be

calculated through the equations (4.9) and (4.10).

1

· 2· · · · · · · ·sending c sending c c c c sendingI Y V H Y Y H H Y H Y V

(4.9)

1

2· · · · · ·receiving c c c sendingV Y H H Y H Y V

(4.10)

Where Yc and H, are calculated through the equations (4.5) and (4.6) and the matrices

Z and Y calculated before for the pipe type cable.

Whereas,

1 1

1

2

2

3

2

3

3 0

0

0

0

C C

S

C

Ssendi

C

n

C

S

C

A

g

V V

V

V V

VV

V V

V

V

(4.19)

The voltages on the sheaths and on the armour are zero as it was explained before,

because they are grounded. Once the equation is solved (4.10), the expected voltage

at the receiving end of the line is shown in the figure below.

Fig. 4.9 Voltage at the receiving end pipe-type cable.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-150

-100

-50

0

50

100

150

Time [s]

Voltage [ k

V ]

Voltage receiving end pipe-type cable

48

Below is represented the voltage comparison between the sending and the receiving

end of the line using a pipe type configuration for the submarine cable.

Fig.4.10 Voltage comparison between the sending end and receiving end pipe

type configuration

In this figure can be observed that the cable presents a Ferranti Effect of 8.1 %, while

the measurement presents an 8%. These results prove that the pipe type model

represents accurately the real measurements. Thus, in chapter 5 an improved model of

the SC is built in PSCAD, considering the limitations of the software.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-150

-100

-50

0

50

100

150Ferranti Effect

Time [s]

Voltage [kV

]

VreceEquations

Vsending

49

5. Description of the PSCAD model

In this chapter the model of the system is built up in PSCAD having into account the

results obtained in chapter 4.

5.1 PSCAD model configuration

Fig. 5.1 Model of the system

The model is composed by an ideal voltage source followed by the short circuit

impedance, a resistance in series with an inductance. The three phase breaker,

connect the short circuit impedance with the 54km land cable. The shunt reactor is

connected to the system at Blaabjerg station. Then, the 2.3 km land cable connects the

onshore with the 42 km submarine cable (its modelling was explained in the previous

chapter).

5.2 Choice of the cable

As it was described in Chapter 3, the most accurate available model is the

Frequency Dependent Model (phase). Thereby, it will be used in this project. As shows

the figure 5.2, PSCAD represents a cable through two components: the cable interface

and the cable configuration.

A

B

C

R=0

C

B

A

BRKA

TimedBreaker

LogicOpen@t0

Ia1

Ib1

Ic1

Ea1

Eb1

Ec1

Ca1

Cb1

Cc1

Sa1

Sb1

Sc1

Ca2

Cb2

Cc2

Sa2

Sb2

Sc2

2.3 kmLand Cable

Ca1

Cb1

Cc1

Sa1

Sb1

Sc1

Ca2

Cb2

Cc2

Sa2

Sb2

Sc2

SeaCable

UcUbUa

Reactor

0.0

00

01

[H]

0.0

00

01

[H]

0.0

00

01

[H]

3 [o

hm

]

Ua1

Ub1

Uc1

Sa1

Sb1

Sc1

Ua2

Ub2

Uc2

Sa2

Sb2

Sc2

54 kmLand Cable

0.0

00

01

[H]

0.0

00

01

[H]

0.0

00

01

[H]

3 [o

hm

]

0.0

00

01

[H]

0.0

00

01

[H]

0.0

00

01

[H]

3.0

[oh

m]

0.0

00

01

[H]

0.0

00

01

[H]

0.0

00

01

[H]

3 [o

hm

]

0.4132 [ohm] 0.03805 [H]

0.4132 [ohm] 0.03805 [H]

0.4132 [ohm] 0.03805 [H]

Ia2

Ic2

Ib2

BRKB

TimedBreaker

LogicOpen@t0

BRKC

TimedBreaker

LogicOpen@t0

Eas

Ebs

EcsIr

a

Irb

Irc

Iblaa

Iblab

Iblac

Era

Erb

Erc

Iseaa

Iseab

Iseac

Ea2

Eb2

Ec2

0.5

2e

-0

06

[F]

0.5

2e

-0

06

[F]

0.5

2e

-0

06

[F]

50

Fig. 5.2 PSCAD components.

While the cable interface is the electrical connection to rest of the net, the cable

configuration allows to define cable parameters like length, material properties, etc.

5.3 Land cables and submarine cable

5.3.1 52 km Land Cable

This cable connects Endrup and Blaabjerg, is modelled in PSCAD using the two

components described above based on the parameters given in the datasheet. These

parameters were given in the Chapter 2 in Table 2.2.

Cable position

As explained in Chapter 4 the cables are laid in a close triangle. The cable layout in

PSCAD can be seen in the next figure:

51

Fig. 5.3 Layout for the 52 km land cable.

The centre of cable #1 lies in 1, 3 m depth. Cables #2 and #3 lie under the cable #1 in

depth 2,3d , which is calculated as:

2 22 2

2,3 1 2 1.3 2·0.0475 0.0475 1.3823 d d r r m (5.1)

Whereas 1d is the depth of cable 1 and r is the cable outer radius. The x-y position of

each cable can be found in the next table.

Cable x-y position

Cable #1 0 – 1.3

Cable #2 -0.047505 – 1.3823

Cable #3 0.047505 – 1.3823

Table 5.1 Laying positions of the cables.

Conductor resistivity

The conductor it is formed by stranded aluminium wires, so that, the resistivity needs

to be increased as these wires cannot be modelled in PSCAD. The resistivity of the

aluminium is 82.8 10 m , and it is increased with formula (4.1). The formula is

presented again:

2 281 20.75

2.8 10 3.156 1200

c c

c

rm

A

Where r1 is the conductor radius and cA is the cross-section area of the conductor.

100.0 [ohm*m]

Relative Ground Permeability:

Ground Resistivity:

1.0

Earth Return Formula: Analytical Approximation

0.02075

Cable # 1

0.04110.042389

0.0475

1.3 [m]

0 [m]

Conductor

Insulator 1

Sheath

Insulator 2

0.02075

Cable # 2

0.04110.042389

0.0475

1.3823 [m]

-0.047505 [m]

Conductor

Insulator 1

Sheath

Insulator 2

0.02075

Cable # 3

0.04110.042389

0.0475

1.3823 [m]

0.047505 [m]

Conductor

Insulator 1

Sheath

Insulator 2

52

Permittivity

It is not possible to model the semiconducting layers directly. Using equation (4.2) the

permittivity is found to be:

2

1' 2.739i

rln

r

bln

a

Where i is the relative permittivity of the insulation, which is formed by XLPE and has

a value of 2.3; r2 and r1 are the inner radius of the sheath and the outer radius of the

conductor respectively; a and b are the inner and outer radius of the insulation.[47]

Sheath thickness

The sheath consists of copper wires and will be implemented as one solid conductor in

PSCAD since it is not possible to model the sheath as wires. In the datasheet it is only

given the cross section area, 95 mm2 . Furthermore, an aluminium sheath of 0.2 mm is

used as a water barrier. The thickness of the copper layer is calculated with the

following formulas, having into account the number of copper wires (n). This n was

obtained counting the wires in a piece of the cable. [22]

2· ·A n r (5.2)

Where r is the radius of each copper wire, which is calculated as:

950.55

· 3.14·97

Ar mm

n (5.3)

Multiplying this radius times two it is obtained the thickness of this layer. Using the

following equation the resistivity of the copper wires is corrected as:

2 2 2 2

3 2, 8 8

, ,

42.21 41.1' 1.724·10 5.272·10 ·

95

sh

s cu s cu

s

r rm

A

(5.4)

Where r3 is the sum of the radius of the dielectric screen plus the thickness of the

metallic sheath. The thickness of the copper sheath is 1.11 mm, with a cross section

area of 290 mm2 and an equivalent resistivity of 85.272·10 ·m .The aluminium sheath

is also modelled as a solid coaxial conductor, but, in PSCAD it is not possible to define

two different conductive layers without an insulation material in between. Thus, the

thickness of the layer is found as the sum of the copper and aluminium sheath. This

sheath is 0.2 mm with a resistivity of 2.83· 10-8 ·m and its area is calculated:

53

2 2

2 1 (5.5)AlA r r

Where r2 is the outer radius of the aluminium sheath and r1 is the outer copper wire

radius. Using equation (5.2):

2 2 2 2 2

2 1 42.41 42.21 53.17 (5 .6 )AlA r r mm

The equivalent resistivity of the coaxial conductor formed by the two sheaths is

calculated as:

84.8939·10 ·Cu Aleq Al

Cu Al Cu

Cu

Al

A Am

A A A A

(5.7)

Cross bonding

The cross bonding is implemented as described in Chapter 2 using an inductance of 1 µH/m for the cable used to cross bond the screens. The ground resistance is set to 3 Ω. The entire 42 km land cable has 32 cross bonding points, but due to the license available in PSCAD, does not allow the required number of nodes to perform the simulation, a simplified model is used. In this simplified model the numbers of cross bonding points are reduced to one cross bonding point. Each segment has a length of 18 km.

Fig. 5.4 Simplified PSCAD modelling of the sheath with cross-bonding.

5.3.2 2.3 km Land cable

The 2.3 km land cable is the same type as the 54 km land cable. Hence, it is

modelled in the same way and using the same parameters named before. In this case

the length of each segment it is set to 0.7667 km. The figure below shows the cross

bonding of this cable.

C101

S1

C2

S2

C3

S3

C101

S1

C2

S2

C3

S3

C102

S1

C2

S2

C3

S3

0.000001 [H]

0.000001 [H]

0.000001 [H]

C102

S1

C2

S2

C3

S3

C103

S1

C2

S2

C3

S3

0.000001 [H]

0.000001 [H]

0.000001 [H]

C103

S1

C2

S2

C3

S3

01

C

Ua1

Ub1

Uc1

Sa1

Sb1

Sc1

Ua2

Ub2

Uc2

Sa2

Sb2

Sc2

03

C

02

C

54

Figure 5.5 Cross bonding points for the 2.3 km land cable.

5.3.3 Submarine cable

This cable is modelled using the same approximations as for the land cable.

Fig. 5.6 Layout of the submarine cable.

The depth of cables 2 and 3 it is found using equation (5.1):

2 22 2

2,3 1 2 1.3 2·0.04245 0.04245 1.3735 2 d d r r m

Cable x-y position

Cable #1 0 – 1.3

Cable #2 -0.0424505 – 1.37352

Cable #3 0.04424505 – 1.37352

Table 5.2 Laying positions of the cables.

The corrected resistivity of the core is calculated with equation (4.1):

Ca1

Cb1

Cc1

Sa1

Sb1

Sc1

C1AB

S1

C2

S2

C3

S3

C1CD

S1

C2

S2

C3

S3

C1AB

S1

C2

S2

C3

S3

C1BC

S1

C2

S2

C3

S3

0.000001 [H]

0.000001 [H]

0.000001 [H]

C1BC

S1

C2

S2

C3

S3

C1CD

S1

C2

S2

C3

S3

0.000001 [H]

0.000001 [H]

0.000001 [H]

Ca2

Cb2

Cc2

Sa2

Sb2

Sc2

AB

C

BC

C

CD

C

100.0 [ohm*m]

Relative Ground Permeability:

Ground Resistivity:

1.0

Earth Return Formula: Analytical Approximation

15.25 [mm]

Cable # 1

37.75 [mm]40.15 [mm]42.45 [mm]

1.3 [m]

0 [m]

Conductor

Insulator 1

Sheath

Insulator 2

15.25 [mm]

Cable # 2

37.75 [mm]40.15 [mm]42.45 [mm]

1.37352 [m]

-42.4505 [mm]

Conductor

Insulator 1

Sheath

Insulator 2

15.25 [mm]

Cable # 3

37.75 [mm]40.15 [mm]42.45 [mm]

1.37352 [m]

42.4505 [mm]

Conductor

Insulator 1

Sheath

Insulator 2

55

2 28 81 15.25

1.724 10 =1.97 10 630

c c

c

rm

A

The permittivity of the insulation is modified using equation (4.2):

2

1'

37.75

15.25

34.75

16.7

2.85

5

7i

rln ln

r

bln ln

a

The sheath it is modelled with a resistivity of 2.2·10-7 Ω·m and 2.4 mm of thickness.

The most outer layer is semiconductive and as this cannot be implemented in PSCAD

its permittivity is approximated as 1000. [7]

In PSCAD it is not possible to surround the three conductors by a common armor, so

the SC module cannot be changed. The improvement of the model is done after this

module.

The difference between the touching trefoil and the pipe-type is that the cable on the

second configuration presents higher capacitance. Thereby, the voltage at the

receiving end on this configuration is higher than in the touching trefoil and it is closer

to the real measurements. This is proved using the equations from the previous

chapter. The obtained results are shown in the figure 5.6 and in figure 5.7 it is shown

the voltage measured at the receiving end.

Fig. 5.7 Receiving end voltage comparison between touching trefoil configuration and

pipe type configuration.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-150

-100

-50

0

50

100

150Voltage receiving end

Time [s]

Voltage [kV

]

touching trefoil

pipe-type

56

Fig. 5.8 Measurement of the receiving end voltage.

Therefore, one way to improve the model is adding the capacitance that the touching

trefoil configuration does not include. This is done connecting capacitors in parallel to

the system. As it was explained in chapter 4, the own capacitances of the core on the

touching trefoil case is Bcctt= Bcs, while in the pipe-type cable is Bccpt = 8·Bcs . Then a

capacitor with a value C, calculated below, is connected in parallel to each phase (see

fig 5.1).

107·1.76·10 ·42.000 51.87C 7·Ccs F

l m Fm

Where l is the length of the SC. These capacitors are connected after the module of

the SC, because if they are connected before they work as filters and the results are

not correct.

5.4 Voltage source and short circuit impedance

5.4.1 Voltage source

The voltage source is modelled as a three phase ideal voltage source followed

by the short circuit impedance. In the simulation is used 159 kV as a voltage value. This

value was obtained in the performed measurements and is used throughout the

project. [5]

0.333 0.334 0.335 0.336 0.337 0.338 0.339 0.34 0.341 0.342 0.343-200

-150

-100

-50

0

50

100

150

200Voltage at the receiving end

Voltage [ k

V ]

time [s]

57

Fig. 5.9 Voltage configuration and signal parameters.

5.4.2 Short circuit impedance

The grid, including the two shunt reactors in Endrup is modelled as an

equivalent impedance as the next figure shows.

RgridLgrid

CgridVsource

Fig. 5.10 Equivalent grid impedance.

In this case the grid capacitance is considered having a small value. Therefore, its

capacitive reactance is calculated as: 1

2CX

j f C

, where f is defined as 50 Hz,

will have a big value. Thus, could be approximated as an open circuit, not being

considered in the calculation of the equivalent reactance.

As it is explained in [22] the short circuit power value in the feeding point in Endrup is

2372 87.91 . This value is considered to be accurate as was measured in the room

control and will be used throughout the project.

58

The influence of the shunt reactors located in Endrup station on the short circuit

impedance is included in the model of the equivalent grid as follows:

In first place, it is calculated the short circuit impedance without the effect of the shunt

reactors:

2 2

,150

1.1 1650.4604 12.617

2372 87.91

nk x y

cUZ R jX j

S

(5.8)

Where Un is the line-line voltage, c is a correction factor and S the apparent power.

Then, according to the “ IEC. Power Transformers part 6: Reactors”, the shunt reactors

are represented as a reactance which is calculated as: [22]

2 2

,80

165340.3

80r

UX j

Q (5.9)

2 2

,40

165680.6

40r

UX j

Q (5.10)

The equivalent reactance of the two reactors, connected in parallel, is calculated as:

,80 ,40

,

,80 ,40

340.3 680.6226.88

340.3 680.6

r r

r eq

r r

X XX j

X X

(5.11)

Therefore, the short circuit impedance is found through a parallel disposition of the

equivalent reactor reactances and the short circuit impedance (without the reactors

effect) calculated before, as:

,150 ,

,150 ,

0.4604 12.617 226.880.4132 11.953

0.4604 12.617 226.88

k r eq

eq x y

k r eq

Z X j jZ R jX j

Z X j j

(5.12)

Where ,150kZ is the equivalent impedance without the shunt reactors and ,r eqX is the

equivalent reactance of the shunt reactors. Then, the short circuit inductance for 50 Hz

is:

11.953

38.05 2

L mHf

(5.13)

In the next figure it is represented the equivalent grid built up in PSCAD:

59

Fig. 5.11 Equivalent grid

5.5 Circuit breaker

The PSCAD model for the three phase breaker at Endrup station is presented.

The main breaker use ‘synchronized switching at zero voltage crossing’ and it is

implemented using three individual ‘Timed breaker logic’ blocks.

Fig. 5.12 Timed breaker logic blocks

In the next figure it is shown the order of switching on of each phase during the

measurements. This plot is done using the available data from the connection

measurements in Endrup.

Fig. 5.13 Connection in Endrup

It can be seen that the first phase to be connected is phase a. Phase c is energised at

30 degrees of the sinusoidal curve. Phase b is the last energised phase, at 60 degrees

of the sinusoidal curve. For 50 Hz the period time is 0.02 s.

A

B

C

R=0 0.4132 [ohm] 0.03805 [H]

0.4132 [ohm]

0.4132 [ohm]

0.03805 [H]

0.03805 [H]

BRKA

TimedBreaker

LogicOpen@t0

BRKB

TimedBreaker

LogicOpen@t0

BRKC

TimedBreaker

LogicOpen@t0

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-200

-150

-100

-50

0

50

100

150

200Voltage-Endrup

Voltage [ k

V ]

Time [s]

Phase a

Phase b

Phase c

60

The switched on is set up to 0.01 seconds for phase a. Phase c is switched on at

0.010.01 0.0133

3 s. Then, phase b it is switched on at

2 0.010.01 0.0167

3

s. The

switching on times is presented in the next table.

Variable Setting

Switch time phase a 0.01 s

Switch time phase b 0.01667 s

Switch time phase c 0.0133 s

Breaker open resistance 1 MΩ

Breaker closed resistance 0.0000001Ω

Table 5.2 PSCAD settings for the main breaker at Endrup station.

5.6 Shunt reactor

In Chapter 3 section 3.2.2 was shown that the measured currents in the shunt reactor were in agreement with the simulated ones, showing almost no difference. Therefore, the shunt reactor model used to perform those simulations is used in this project. A brief description of the model of the 80 MVar shunt reactor connected in Blaabjerg is

developed in this section. In order to get deeper details about its modelling, the reader

is referred to [22, pg 37].

The shunt reactor has three coils that are mounted on a five legs iron core. These legs

have air gaps in order to make linear the inductance behaviour and therefore avoid

saturation. The layout of the shunt reactor is shown below:

Fig. 5.14 Five legs shunt reactor layout. [22]

Shunt reactor models are not available in PSCAD/EMTDC, such models needs to be

created having into account the following characteristics.

61

Losses

Losses must be taken into account. These losses consist on Joule loss, iron loss and

additional loss. Joule losses are consequence of current flowing, therefore, are current

dependent. Iron losses consist of Eddy currents and hysteresis losses caused by the

changing magnetic field, being voltage dependent. The additional losses consist on all

the other losses; the most important are the stray losses. These are caused by the

interaction of the flux leakage with metallic parts.

Self inductance

The self inductance of the reactor is calculated as:

2

21

2

UL R

f I

(5.14)

WhereU , I and f , are the voltage, current and frequency measured with the winding

resistance known. The values for the self inductance are given in the ABB test report.

[56]

Mutual inductance

There is mutual coupling between the coils of each phase, as these are mounted in the

same iron core. The mutual inductance describes the voltage induced in one phase,

caused by the changing current in other phase. This value is reduced with the air gap in

the core. The mutual couplings were measured magnetizing all phases in turn and

measuring the induced voltages in the other two phases. These mutual couplings were

given in the test report. [56, pg 27]

Magnetic Saturation

The saturation characteristic of the shunt reactor is shown in the next picture:

62

Fig. 5.15 Saturation characteristic of the shunt reactor. [56, pg 26]

As it can be appreciated the shunt reactor is unsaturated until it reaches approximately

1.4-1.5 per unit current. In the report made by the external company the voltages

were simulated with 2.07 pu at Blaabjerg for two phase short circuit with earth fault at

the 80 MVAr Endrup reactor. Therefore, the saturation must be implemented.

The model must take into account all these characteristics. PSCAD does not have an

available model for this purpose. Thereby, to include all the characteristics (losses,

mutual couplings and saturation) coupled wires and a transformer are connected in

series. In the coupled wires are placed the resistances and the mutual inductances,

and in the transformer are placed leakage reactance and saturation effects. [22, pg 48]

Fig. 5.16 Layout model shunt reactor.

In the next figure the input parameters of the coupled wires are given. [22]

Uc

Ub

Ua

m

#1 #2

#1 #2

#1 #2

63

Fig. 5.17 Individual components of the mutual wire configuration.

The leakage reactance needs to be calculated as is an input parameter of the single

phase transformer. The leakage reactance must be in pu, then the impedance base it is

calculated as: [22, pg 49]

2 2170361

80b

UZ

S (5.15)

Where U is the nominal voltage of the reactor and S is the apparent power. The

leakage reactance is calculated dividing ωL over this value.

64

Fig. 5.18 Single phase transformer configuration.

The power rating of the single phase transformer is set up as one third of the total

reactor power.

The values for the saturation are set up as in the test report.

Fig. 5.19 Input parameters for the magnetic saturation.

65

5.7 Simulation settings

The time step in the project settings must be chosen carefully. On one hand, if

the time step it is too big, the simulation can be distorted; on the other hand, if too

small, could be time consuming. The smallest segment length used in the model is

766.7 m, so the time step will be small. Manitoba Research Centre Inc states: “A good

rule of thumb is to use a calculation time step of one half the propagation time along

the shortest of the main conductors under study”. [25, pg 33]

Assuming a travelling speed of 3.108 m/s (speed of light) of the travelling wave through

the smallest segment, the travelling time is calculated as:

6

0.76671.2778

2 3 10

kms

km

s

. Therefore the time step is selected as 1 µs.

Fig. 5.20 Project settings.

66

6. Results and validation of the model

In the first part of this chapter are presented the results from the simulation of the

model described in the previous chapter. Then, a sensitive analysis of the analytical

solution from the chapter 4 is done, to prove the accuracy of the results and to study in

which way they could be improved.

6.1 Results of the improved model in PSCAD

In this subchapter the results from the improved model are shown.

Fig. 6.1 Difference between the sending and receiving end voltage of the improved

model.

It is noticed a Ferranti of 18.1 %, which is different from the one obtained in the

measurements (8%). Furthermore, it is noticed that the voltage at the receiving end is

bigger than the one obtained in the measurement and through the use of equations

(see figures 6.2 and 6.3). This effect is caused due to the capacitors introduce an

increase in the voltage of the whole system, fact, that invalidates the proposed

improved model.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-300

-200

-100

0

100

200

300Ferranti effect - Improved model

Voltage [ k

V ]

time [s]

Sending end

Receiving end

67

Fig. 6.2 Voltage calculated at the receiving end using the equations from chapter 4.

Fig. 6.3 Voltage measured at the receiving end.

6.2 Analysis of the pipe type cable model

The purpose of a sensitive analysis is to observe how the results can change by

varying any of the input parameters. In this way can be studied which parameters

strongly affects the final results and consequently they should be chosen carefully. In

this case the voltage at the receiving end is studied.

Changes on the armour properties

The possible changes in the voltage at the receiving end that can be introduced by

changes on the material properties of the armour are studied below. Table 6.1

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-150

-100

-50

0

50

100

150

Time [s]

Voltage [ k

V ]

Voltage receiving end pipe-type cable

0.333 0.334 0.335 0.336 0.337 0.338 0.339 0.34 0.341 0.342 0.343-200

-150

-100

-50

0

50

100

150

200Voltage at the receiving end

Voltage [ k

V ]

time [s]

68

presents the results of the voltage peak on phase a, increasing the permittivity of the

armour.

From chapter 4 and the appendix it is determined that the armour susceptance is

equal to 3

1

aa a cia

i

B B B

. Thus, the way to increase the permittivity of the armour is

multiplying , aB by a factor, fYaa , as:

3

Yaa

1

f · aa a cia

i

B B B

(6.1)

fYcs Vapeak [kV]

1 145.4

100 145.4

1000 145.4

10000 145.4

Table 6.1 Peak voltage values increasing the permittivity of the armor.

From Table 6.1 it is observed that changes on the armour’s susceptance do not

affect the voltage at the receiving end. That can be explained through the flown

currents along the armour shown in figure 6.4 and 6.5

Fig. 6.4 Current comparison at the sending end between the core and the armour

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-4

-3

-2

-1

0

1

2

3

4Current Comparison

Time [s]

Curr

ent [A

]

Core

Armour

69

Fig. 6.5 Current on the armour

The current along the armour is close to zero, despite of increasing the susceptance of

the armour, which will not affect the core voltage results. That proves that the armour

does not affect the behaviour of the cable.

Changes on the sheath properties

In the same manner, in table 6.2 are presented the results of the voltage peak in phase

a increasing the permittivity of the sheath.

From chapter 4 and the appendix it is determined that the sheath susceptance is equal

to 3

1

ss s cjsi

j

B B B

. To increase the permittivity of the sheath , sB is multiplying by a

factor, fYss:

3

Yss

1

6.f 2·ss s cjsi

j

B B B

fYss Vapeak [kV]

1 145.4

100 145.4

1000 145.4

10000 145.4

Table 6.2 Peak voltage values increasing the permittivity of the sheath.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-3

-2

-1

0

1

2

3x 10

-4 Current on the armour

Time [s]

Curr

ent [A

]

70

The voltage at the receiving end keeps equal despite of the increasing in the

permittivity of the sheath. Thus, the sheaths do not affect the behavior of the cable.

In figure 6.6 the current flowing through the core and the sheath in phase a are

represented. As the sheath is bonded, it current is almost zero.

Fig. 6.6 Sending end currents flowing through the sheath and the core.

Changes on the insulation properties

It is proved that increasing the permittivity of the insulation the voltage at the

receiving end also increases. This is shown in table 6.3.

Increasing the permittivity of the insulation supposes an increase of the capacitance

between the core and the sheath (Ccs) and consequently, all the susceptance matrix

would change (see appendix).

This has no sense because the pipe-type model should keep the real characteristics of

the cable that means that the permittivity of the XPLE ( 2.3) should not be modified.

fYcs Vapeak [kV]

1 145.4

3 165.6

8 240.8

10 286

Table 6.3 Peak voltage values changing the insulation properties.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-4

-3

-2

-1

0

1

2

3

4

Time [s]

Voltage [kV

]

Current at the sending end

Core

Sheath

71

7. Conclusions

This report studies the steady–state behaviour of the offshore wind farm,

Horns Rev 2, where the power transmission is done by a 42 km submarine cable

connected to a 57.9 km land cable. The simulation results of the system built up in

PSCAD in a preliminary report show a mismatch between them and the real

measurements during the steady-state, the energization and the de-energization of

the transmission system. Because of the limited project time, the study is focused on

the steady-state behaviour of the transmission system.

Comparing the measured points results with the ones from the simulations is

demonstrated that the land cable, the grid and the shunt reactor models in PSCAD are

accurate. In this way it is concluded that the unexpected Ferranti Effect from the

simulations (1.7% while the measurements show around 8%) should be caused by the

submarine cable (SC).

PSCAD does not allow the modelling of the SC as in reality, based on three conductors

with a common armor (pipe –type cable). Thereby, on the previous report it is

modelled in a touching trefoil configuration despite the mistakes that this

simplification might have introduced. An analytical method based on equations to

calculate voltages and currents between two points using the cable impedances and

susceptances matrices is developed to prove the PSCAD results for the touching trefoil

case. With a 0.62% of error between the analytical results and the simulated ones for

the voltage at the receiving end of the cable, the method is validated. Thus, this

method is used to calculate the expected voltages and currents for the pipe-type cable.

The pipe-type impedance and susceptance matrix should be discussed carefully

because of two reasons. On one hand, the armour constitutes an extra bonded layer

added to the touching trefoil configuration and that could affect the system

transmission behaviour. On the other hand, there is not a clear example for pipe-type

cable with both the sheaths and the armour grounded on the analytical method. Thus,

the susceptance matrix calculations are supported by a finite element study on a

section of the cable to determinate the capacitance between the layers. Based on the

results of this study, it is concluded that the pipe-type cable presents higher

capacitance than the touching trefoil configuration.

Once calculated the expected voltage at the receiving end for the pipe-type it is

observed an 8.1% of Ferranti Effect on the cable. That fact proves two things; firstly,

the analytical results for the armoured cable are similar to the measurements (8% of

Ferranti Effect). Secondly, it is necessary to improve the SC model of the previous

report.

72

The difference between the two configurations is based on the different capacitance

presented between the layers. Therefore, a way to improve the model (taking into

account that in PSCAD it is not possible to model the common armour surrounding the

three conductors) is to connect in parallel to the core of each phase the capacitance

difference between the touching trefoil and the pipe-type. The results show a large

voltage at the receiving end. This is because adding capacitors at the end of line

increases the voltage of the whole system. Consequently, the improvement of the

cable is not obtained adding the capacitance difference connected in parallel.

A sensitive analysis of the analytical solution is done to prove the accuracy of the

analytical results and to study in which way they could be improved. It is shown that

neither the own permittivity of the armor nor the one of the sheaths affects the final

results. Only the permittivity of the core insulation is the one which affects all the

results.

7.1 Future work

Below are listed issues that could be investigated in a future work:

- Decrease the difference between the measurements and simulations, regarding the steady state behaviour.

- Analyse the behaviour of the system when it is de-energized by comparing simulations and measurements.

- Study another way to improve the submarine cable model taking into account the limitations of the software.

73

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78

A. Appendix submarine cable parameters calculations

The figure below represents the pipe-type cable, where the radius used in the calculations is indicated. In the case of study neither the plastic sheath nor the armour are considered. Each phase presents the core, the core insulation, the sheath and the sheath insulation. The armour is common to the three conductors with a radius of 104mm.

Fig. A-1 Cross section of a pipe type cable. [46, pg 142]

In table A-1 the values of the radius are given.

Radius mm

ric 0

roc 15.25

ris 37.75

ros 40.15

ria 42.45

roa 104

Table A-1 Different radius of each layer.

The cable is electrically described by its series impedance and shunt admittance.

79

Series impedance

The series impedance is composed of a resistor and an inductance. In order to calculate these parameters, it is required to have knowledge of the conductor material, the physical dimensions, construction and soil resistivity. DC resistance

The cable under investigation (TKRA 170 kV 3x 1 x 630 mm2) has a core made out of

copper wires; therefore its resistivity is modified using the following formula: [11]

2' · · oc

copper

r

A

(A-1)

Where the resistivity of the copper, roc is is the outer radius of the conductor and

copperA is the cross section area of the conductor.

The DC resistance is given by:

'

( ) 20

1000 1 ( 20) dcR T

A km

(A-2)

Where ' is the modified resistivity of the conductor, A is cross-section of conductor,

20 is the resistivity at 20º and T is temperature of the conductor (°C).

'

( )

1000 dcR

A km

(A-3)

AC resistance

The cable consists of many layers. There are three metallic layers (core, sheath,

armor). Each of these layers has an AC resistance, which is calculated as:

( ) ( ) 1 ( ) ac dc s pR R y k kkm

(A-4)

Where y is equal to 1, because the cable is three core type, ,sk pk are skin and

proximity effect factors, respectively. They can be calculated through the following

expressions.

80

4

4

2

0 2.80.8· 192

0.0563· 0.0177· 0.136 2.8 3.8

0.354· 0.73 3.8

p

zz

z

z z z

z z

k

(A-5)

Whereas z it is calculated as 4

8

10

z

dc

f az

R

for a frequency of 50 Hz and za for

copper conductors is equals to 1.

The proximity factor is calculated as:

2

2 2

2.9· ·

1.18· · 0.312·

0.27

c

c c

p

dF p for twocoreand two singlecorecable

S

d dF p for threecoreand three singlecore

S S F p

k

cable

(A-

6)

Where 4

4 0.8· 192

pF p

p

, and

4

8

10

p

dc

f ap

R

. As the core is stranded

pa =0.8.

Having into account the AC resistance, the self impedances of the core, sheath and

armour, are calculated, as well as, the mutual impedances between core and sheath or

sheath and amour.

The own core impedance is the same for the three conductors because they are equals,

it is obtained as:

2 4 4

( ) ·10 · 4 ·10 · · , log 4

c erccc c ac oc ic e

oc

µ DZ R f j f r r

r km

(A-7)

The own impedance of the three sheaths can be calculated through the expression:

2 4 4

( ) ·10 · 4 ·10 · · , log 4

c ercss S ac oc is e

oc

µ DZ R f j f r r

r km

(A-8)

Where cµ is the relative permeability of the armour and , oc isf r r is calculated as:

2 4

22 22 2

2· 4·, 1 ·log

oc ic ococ ic e

oc is icoc ic

r r rf r r

r r rr r

(A-9)

The mutual impedance between core and sheath or sheath and armour is expressed as:

81

2 4 4·10 · 4 ·10 · log ercij e

ij

DZ f j

S km

(A-10)

Where ercD is the equivalent distance for earth return conductor. If the conductors

belong to the same cable ijS is the geometric mean distance defined as

,2

os isi j

r rS

. If the conductors belong to different cables ijS is the distance

between the centres. The ercD is calculated as:

1 .30912 eercD m

f

(A-11)

Whereas e is the average earth resistivity with a value of 100 ·m .

Then the impedance matrix for a three core armoured cables can be written as:

1 1 1 1 1 2 1 2 1 3 1 3 1

1 1 1 1 1 2 1 2 1 3 1 3 1

2 1 2 1 2 2 2 2 2 3 2 3 2

2 1 2 1 2 2 2 2 2 3 2 3 2

3 1 3 1 3 2 3 2 3 3 3 3 3

3 1 3 1 3 2 3 2 3 3

C C C S C C C S C C C S C A

S C S S S C S S S C S S S A

C C C S C C C S C C C S C A

S C S S S C S S S C S S S A

C C C S C C C S C C C S C A

S C S S S C S S S

p

C

t

Z Z Z Z Z Z Z

Z Z Z Z Z Z Z

Z Z Z Z Z Z Z

Z Z Z Z Z Z Z

Z Z

Z

Z Z Z Z Z

Z Z Z Z Z Z

3 3 3

1 1 2 2 3 3

A- 12

S S S A

AC AS AC AS AC AS AA

Z

Z Z Z Z Z Z Z

While the impedance matrix for the touching trefoil configuration is the same as for

the pipe-type cable without the row and column for the armour.

1 1 1 1 1 2 1 2 1 3 1 3

1 1 1 1 1 2 1 2 1 3 1 3

2 1 2 1 2 2 2 2 2 3 2 3

2 1 2 1 2 2 2 2 2 3 2 3

3 1 3 1 3 2 3 2 3 3 3 3

3 1 3 1 3 2 3 2 3 3 3 3

C C C S C C C S C C C S

S C S S S C S S S C S S

C C C S C C C S C C C S

S C S S S C S S S C S S

C C C S C C C S C C C S

S C S S S C S S S

t

C S

t

S

Z Z Z Z Z Z

Z Z Z Z Z Z

Z Z Z Z Z Z

Z Z Z Z Z Z

Z Z Z Z Z Z

Z Z Z Z Z Z

Z

A- 13

Shunt admittance

The capacitance of the cable depends on the type of insulation (its relative

permittivity) and the diameter of the conductor and insulation.

82

Pipe Type Cable

If 1cI is the current earth return of the core cable, described as:

c1 c1a c1c2 c1s1 c1s2 c1s3 c1c3I I I I I I I (A 14)

Where:

ciaI is the current flown between the armour and the core i.

cisjI is the current flown between the core i and the sheath j.

1 3c cI is the current flown between the core i and the core j, as long as i≠j.

c1a c1c2 c1s1 c1s2 c1s3 c1c3c1

c1a c1c2 c1s1 c1s2 c1s3 c1c3

V V V V V VI (A 15)

1 1 1 1 1 1

jωC jωC jωC jωC jωC jωC

c1 c1 a c1 c2 c1 s1 c1 s2 c1 s3 c1 c3

c1

c1a c1c2 c1s1 c1s2 c1s3 c1c3

V V V V V V V V V V V V V (A 16)

1 1 1 1 1 1Y

jωC jωC jωC jωC jωC jωC

As the sheaths and the armour are grounded voltages aV , 2 , sV 3sV , 1sV are 0.

c1c1 c1a c1 c2 c1c2 c1 c1s2 c1 c1s3 c1 c1s1 c1 c3 c1c3

c1

V V ·jB V V jB V ·jB V ·jB V ·jB V V jB A-17

Y

c1 c1 c1 c1a c1c2 c1s2 c1c3 c1s3 c1s1 c2 c1c2 c3 c1c3V ·jB V jB jB jB jB jB jB V ·jB V ·jB (A 18)

c1 c1 c1 c1a c1c2 c1s2 c1c3 c1s3 c1s1 c2 c1c2 c3 c1c3V ·B V B B B B B B V ·B V · B (A 19)

In this way is proved that the own susceptance of the core 1 (analogously for the other

phases) is equal to:

1 2 2 3 3 1 (A 20)c cia cic cis cic cis cisB B B B B B B

And is verified the negative sign of the susceptance between cores.

The results from the finite element study (Quick Field software) shows that the

capacitance between the sheaths and between the sheaths and the armour (for the

pipe type configuration) are not considered due to both layers presents the same

83

potential for each time instant, as they are bonded. Consequently, the capacitances

between the different layers on a section of the cable can be represented as:

C1 C3S3

S2S1 C2

A

Fig. A-2 Electrical scheme of the cable.

Figure A-2 represents the capacitances between the layers taking into account the

simplification named in chapter 4, where is considered that the voltages in the sheaths

and in the armour are 0 kV along the 42km SC. Thus, susceptance matrix terms can be

described as:

3 3

1

cici cia cisj cicj

j j i

B B B B

(A 21)

(A 22)cicj cisi cjsiB B B

3 3

1 1

(A 23)sisi s cjsi asi ss cjsi

j j

B B B B B B

cisj csB B (A 24)

(A 25)cia cisi asi csB B B B

3

1

(A 26)aa a cia

i

B B B

The capacitance between the core and the sheath is calculated using the following expression: [8]

84

0.05563/ /

log

cscs

ise

oc

C F km phaser

r

(A-27)

Where cs is the relative permittivity of the insulation, isr and ocr are the inner radius of

the sheath and the outer radius of the conductor respectively. In this formula the

semiconductive layers are not taken into account, the permittivity needs to be

modified as follows:

2

1' A 28i

rln

r

bln

a

Where i is the relative permittivity of the insulation, r2 and r1 are the inner radius of

the sheath and the outer radius of the conductor respectively; a and b are the inner

and outer radius of the insulation. [43]

The capacitance between ci (core i) and a (armour) is the same as the capacitance

between ci and any of the sheaths (fig.A-2) , as the armour and the sheath are at the

same potential and the capacitance between them is not considered.

The equivalent capacitances between cores are equal to a parallel connection, as the

voltages on the sheaths and the armour are considered 0 along all the length. Thus;

2 29cicj csB B A

The own capacitance of the sheath si is calculated with the capacitance of the sheath i

and the sum of the capacitances between this sheath and the cores. Cs is calculated as

the following expression from [8]:

0.0556325· ( 30)

log

ss

iae

os

F

kmC Aphaser

r

The own capacitance of the armour is calculated through the capacitance of the

armour, Ca, and the sum of capacitances between the armour and the cores. Ca is

calculated in the following expression as: [57]

0.0556325·

( 31)

log

aa

oae

oa p

F

kmC Aphaser

r t

85

Thus, susceptance matrix of the pipe-type cable SC can be calculated like:

Touching trefoil cable

The susceptance matrix of the touching trefoil configuration, Ytt is presented below:

(A- 33)

2· 2·

2· 2·

2· 2

8·

3· 0 0 0

8·

0 3· 0 0

8·

0 0 3· 0

0 0

·

0 3·

B B B B B B Bcs cs cs cs cs cs cs

B B B Bcs cs cs cs

B B B B B B Bcs cs cs cs cs cs cs

B B B Bcs cs cs cs

B B B B B B Bcs cs cs cs cs cs cs

B B B Bcs cs

Bs

pt Bs

cs cs

B B B Bcs cs cs cs

Bs

Ba

Y

( 32)A

0i 0i 0i 0i

0i 0i 0i 0i

0i 0i 0i 0i

0i 0i 0i 0i

0i 0i 0i 0i

0i 0i 0i 0i

Bcs Bcs

Bcs Bss

Bcs Bcs

tt

Bcs Bss

Bcs Bcs

Bcs Bss

Y