Assessment of 42 Km, 150 kv AC submarine cable at the Horns Rev 2 HVAC wind farm

Transcription

1 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: 3 RD SEMESTER EPSH (M.SC) PROJECT PERIOD: ECTS: 22 SUPERVISOR: FILIPE MIGUEL FARIA DA SILVA CLAUS LETH BAK PROJECT GROUP: EPSH 3, GROUP 901 SYNOPSIS: 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. 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. 2

3 Content 1. Introduction.5 2. System description Turbines Cables Grounding of the cable Connection of the subsystems Problem analysis Cable models Problems associated during the energization of the cable Problems in steady state Effect of the cable on the grid Problem statement Aim of the project Solution method Comparison between theory equations and PSCAD results Submarine cable model in PSCAD Receiving end voltage of each configuration Description of the PSCAD model PSCAD model configuration Choice of the cable Land cables and submarine cable Voltage source and short circuit impedance Circuit breaker 57 3

4 5.6 Shunt reactor Simulation settings Results and validation of the model Results of the improved model in PSCAD Analysis of the pipe type cable model Conclusions Future work Literature.74 A Appendix submarine cable parameters calculation.79 4

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 CO 2 and oil prices, its aim is to achieve the long objective of increasing the wind production to 50 percent by 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 5

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. 6

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 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] 7

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 The centre point of the blade was placed 68 metres above the sea level. The length of the turbine below sea level is between metres. With a blade diameter of 93 metres the total length of the wind turbine above the sea level is 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] 8

9 Submarine system cable transports the produced electricity to the shore. Fig. 2.3 Distribution of the 13 rows of wind turbines. [4] 9

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 mm 2.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 10

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 mm 2. 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 11

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 mm 2. 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] 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 mm 2. 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 mm 2. 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. 12

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: Data of the land cable. Fig. 2.6 Laying of the 150 kv land cable Conductor Conductor screen Parameter Unit Value Outer radius Material Thickness Outer radius mm - mm mm Aluminium Thickness mm 17 13

14 Dielectric Dielectric screen + swelling tape Metallic sheath Water barrier longitudinal Water barrier radial Outer covering Outer radius Material Thickness Average outer radius Thickness Average outer radius Material Cross section Thickness Average outer radius Thickness Average outer radius Thickness Average outer radius Material mm - mm mm mm mm - mm 2 mm mm mm mm mm mm - Table 2.2 Land cable data [22] 39.5 XLPE Copper PE 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 Typical application limiter(surge arrester) 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 14

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] 15

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. 16

17 Fig 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 17 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 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] 18

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 at both ends. The inductance and capacitance however, are 4 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 dv ZYV 2 dx (3.1) 2 di YZV 2 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 brokenup into modes. So, the resulting system of n differential equations is solved through a modal analysis. 19

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. V mode Q t V (3.3) phase I Q 1 I (3.4) mode phase 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 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 20

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] Vin S L Vc IL C 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: f 0 1 (3.1) 2π L C l km 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 V c 2 km 21

22 Voltage [ kv ] Voltage [ kv ] will match the source voltage at different points for the system natural frequency in each cycle. Therefore, the amplitude of V c will change for each cycle. [13] The comparison voltage in the sending end between the measurements (V endrup ) and the simulation results presents an error of 1.5%. This is shown in the figures 3.5 and Fig Sending end voltage - measurement Phase a Phase b Phase c Time [s] Fig. 3.3 Measured sending end voltage Sending end voltage - PSCAD Phase a Phase b Phase c Time [s] Fig 3.4 Simulated sending end voltage during energization. 22

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 (I c ) 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: Ic UCl (3.2) This equation can also be expressed as: I Ul (3.3) Where l the length of the cable, ω is is the angular frequency, c r ε r 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 U Q (3.4) ωl 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. 23

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. 24

25 Current [ ka ] Phase b Measurement PSCAD Time [s] Zero missing phenomenon Fig.3.6 Comparison shunt reactor current in phase b). 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] Vin S IBRK Vc IL L IC C Fig.3.7 L-C parallel circuit. The AC current flowing through the cable will be ideally 90 0 leading the voltage. The opposite will occur with the current flowing through the shunt reactor (90 0 lagging). They cancel out each other and the shunt reactor compensates the reactive power generated by the cable. [13] 25

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 90 0 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 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: 26

27 Current [ ka ] Current [ ka ] The DC component is damped faster in the real system than in the simulated one Current - Shunt reactor - measurement Phase a Phase b Phase c Time [s] Fig.3.9 Current measured in the shunt reactor Current - Shunt reactor-pscad Phase a Phase b Phase c Time [s] Fig Shunt reactor simulated current. 27

28 Current [ka] Current [ ka ] For the sending end the current peak values are slightly smaller in the simulation. Sending end current - measurement 0.5 Phase a Phase b Time [s] Fig.3.11 Sending end measured current. Phase c) it is not shown due to it was not measured. 0.5 Sending end current - PSCAD Phase a Phase b Time [s] Fig Sending end simulated current. Phase c) it is not shown due to it was not measured. 28

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] R L Us C1 C2 Ur Fig Pi model of the cable regardless the shunt reactor. The voltage in the receiving end can be found on basis of fig The capacitance in the sending end has no influence on the voltage drop along the cable. U r is defined as: 2 j Z U U C U j jl C C 2 r s s Z 2 C 2 Zseries (3.5) Reorganazing this equation we can isolate U r as: U r 1 U s C L 2 2 (3.6) Where L is the cable s inductance, C 2 is the cable s capacitance, U s sending voltage, U r 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: 29

30 Voltage [ kv ] Voltage [ kv ] Comparison - Sending end - Receiving end - Measurement Sending Receiving Time [s] Fig 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 Comparison - Sending end - Receiving end - PSCAD Sending Receiving Time [s] Fig 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. 30

31 Voltage [ kv ] Voltage [ kv ] Comparison - Sending end - Receiving end - PSCAD Sending Receiving Time [s] Fig Wider view of the figure The voltage comparison in the receiving end for phase a) is shown in the figure In this figure the difference between the simulation and the measurement is noticed and estimated to be 4.7%. [5] Phase b Measurement PSCAD Time [s] Fig Voltage comparison between measurement and simulation at the receiving end. 31

32 Voltage[kV] Conclusion The conclusions from the comparisons named before are explained using the figure 3.19, where A, B and C are the measurement points. Endrup Vgrid 400 kv 150 kv CB1 land cable 55.4 km land cable 2.3 km sea cable 42 km Zgrid Horns Rev II A B B C 80 MVar Blaabjerg Fig 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 Sending end voltage-connection Phase a Phase b Phase c Time [s] Fig Measurement of the onshore voltage during cable connection. 32

33 Voltage[ kv ] Sending end simulated voltage Phase c Phase b Phase a Time[s] Fig 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. 33

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. 34

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. Ground Resistivity: [ohm*m] Relative Ground Permeability: 1.0 Earth Return Formula: Analytical Approximation Cable # [mm] Cable # 1 0 [m] Cable # [mm] [m] 1.3 [m] [m] Conductor Insulator 1 Sheath Insulator 2 Conductor Insulator 1 Sheath Insulator 2 Conductor Insulator 1 Sheath Insulator [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] 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: Where c is the increased resistivity, 2 r1 c c (4.1) A c c is the resistivity of the copper core, (nominal) cross sectional area of the core and r 1 is the radius of the core. [45] A c is the 35

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: r 2 ln ' r 1 i b ln a (4.2) Where i is the relative permittivity of the insulation, r 2 and r 1 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 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 st Conducting layer Outer radius Resistivity Relative permeability 1 st Insulation layer Outer radius Relative permittivity Relative permeability 2 nd Conducting layer Outer radius Resistivity Relative permeability 2 nd Insulation layer Outer radius Relative permittivity Relative permeability mm Ω m mm mm Ω m mm 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. 36

37 Fig km 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 37

38 consists in compare the voltage at the receiving end (V receiving ) of the simulations with the one calculated through the equations from [39] and [54]. In order to calculate V receiving is necessary to solve this system of equations: I Y V H Y V I (4.3) receiving c receiving c sending sending I Y V H Y V I (4.4) sending c sending c receiving receiving The characteristic admittance, Y c 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 l Y Z H e e (4.6) The current I receiving 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 Y V H Y V I (4.7) c receiving c sending sending I Y V H Y V (4.8) sending c sending c receiving Hence, solving this system of equations both voltage at the receiving end and current in the sending end can be obtained. In the subchapter (three-core in touching trefoil) is presented the V receiving 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 (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. 38

39 4.2.1 Three Core in touching trefoil In the touching trefoil configuration the sheaths (S i) 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: VC1 C1 e b b a b b IC1 V S1 S1 b e b b a b I S1 V C2 C2 b b e b b a I C2 VS2 S2 a b b f b b IS2 V C3 C3 b a b b f b I C3 V S3 b b a b b f I S3 S3 (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: Z 8.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 3.3e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 8.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 3.3e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 8.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 3.3e e-4i *Ω/m+ 39

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. Y 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 [S/m] Voltage comparison Solving the system equation (4.7 and 4.8), V receiving and I sending can be calculated through the following expressions: Whereas: 1 I Y V 2 H Y Y H H Y H Y V (4.10) sending c sending c c c c sending 1 V 2 Y H H Y H Y V (4.11) receiving c c c sending V sending VC1 VC1 V S1 0 V C 2 V C 2 VS 2 0 V V C3 C3 VS 3 0 (4.12) V sending is zero in the sheaths because they are grounded. 40

41 Voltage [kv] The figure below shows the voltage comparison in the receiving end of the line for the core conductor of the phase a) Voltage receiving end equations simulations Time [s] Fig. 4.4 Comparison between equations and simulations results for the V receiving in the phase a. Due to the V receiving 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 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. 41

42 Impedance matrix To calculate the Z matrix the equations from the previous section are used again, adding the self- impedance of the amour Z aa. The relationship between voltage and currents for three core armoured cable configuration is defined as follows: VC1 e a b b b b c IC1 V S1 a f b b b b c I S1 V C2 b b e a b b c I C2 VS2 b b a f b b c IS2 V C3 b b b b e a c I C3 VS3 b b b b e a c IS3 V c c c c c c d I A A (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 µ a (permeability of the armor) in its calculation. The self- impedance of the amour including earth return is given by: a, D erc Zaa R f j f xf r a ac oa ria loge 4 roa km (4.14) Whereas, Ra ac is the ac resistance, f is the operation frequency (50 Hz) roa, r ia are the outer and the inner radius of the armour respectively and Derc 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, µ a, 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 µ a = 1, or µ a = 10. The self impedance of the amour for both cases, are presented below: µ a =1 Z 6.096e e 004 i / m aa µ a =10 Z 6.096e e 004 i / m aa 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 µ a =1. 42

43 4.9e e-4i 3.3e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i z 9.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 9.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 3.3e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 9.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 3.3e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 4.9e e-4i 6.1e e-4i *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= 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, 43

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: 1 1 W E dv C V V ( 1 2 ) (4.15) The voltage boundary condition must be an instantaneous value of the nominal voltage (159 kv). Taking the maximum V a (t= 0), as a possible value, the voltage condition imposed is: Va cos 2 f t 0 kv kv kv (4.16) Vb 159 cos 2 f t 120 kv 159 cos 120 kv kv (4.17) Vc 159 cos 2 f t 120 kv 159 cos 120 kv kv (4.18) 3 3 The voltage distribution on the section of the cable once the model is meshed and solved is presented in fig

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

46 S1 C2 S2 C1 S3 C3 A Fig. 4.8 Electrical scheme of the cable (all the capacitors have a value equal to C cs ). The susceptance matrix Y, is shown below and its terms are described in the appendix. Y 4.43e 7i 5.54e 8i 1.11e 7i 5.54e 8i 1.11e 7i 5.54e 8i 5.54e 8i 5.54e 8i 3.14e 4i 5.54e 8i e 8i e 7i 5.54e 8i 4.43e 7i 5.54e 8i 1.11e 7i 5.54e 8i 5.54e 8i 5.54e 8i e 8i 3.14e 4i 5.54e 8i e 7i 5.54e 8i 1.11e 7i 5.54e 8i 4.43e 7i 5.54e 8i 5.54e 8i 5.54e 8i e 8i e 8i 3.14e 4i e 8i e 8i e 8i e 7i [S/m] 46

47 Voltage [ kv ] 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 I Y V 2 H Y Y H H Y H Y V (4.9) sending c sending c c c c sending 1 V 2 Y H H Y H Y V (4.10) receiving c c c sending Where Y c 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, V sending VC1 VC1 V S1 0 V C 2 V C 2 VS 2 0 V C3 V C3 VS 3 0 V A 0 (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. 150 Voltage receiving end pipe-type cable Time [s] Fig. 4.9 Voltage at the receiving end pipe-type cable. 47

48 Voltage [kv] 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 Ferranti Effect VreceEquations Vsending Time [s] 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. 48

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 PSCAD model configuration BRKA Timed Breaker Logic BRKB Timed Breaker Logic BRKC Timed Breaker Logic Reactor Ua Ub Uc Irc Irb Ira A Ia1 Ua1 Ua2 Iblaa Ca1 Ca2 Iseaa Ca1 Ca2 Ia2 R= [ohm] [H] Eas B [ohm] [H] Ebs C [ohm] [H] Ecs A B C Ib1 Ic1 Ea1 Eb1 Ec1 Ub1 Ub2 Uc1 Uc2 54 km Land Cable Sa1 Sa2 Iblab Iblac Era Erb Erc Cb1 Cb2 Cc1 Cc2 2.3 km Land Cable Sa1 Sa2 Iseab Iseac Cb1 Cc1 Sa1 Sea Cable Cb2 Cc2 Sa2 Ib2 Ic2 Ea2 Eb2 Ec2 Sb1 Sb2 Sb1 Sb2 Sb1 Sb2 Sc1 Sc2 Sc1 Sc2 Sc1 Sc2 0.52e-006[F] 0.52e-006 [F] 0.52e-006 [F] [H] [H] 3.0 [ohm] [H] [H] [H] 3 [ohm] [H] [H] [H] 3 [ohm] [H] [H] [H] 3 [ohm] [H] 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. 49

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 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: 50

51 Ground Resistivity: [ohm*m] Relative Ground Permeability: 1.0 Earth Return Formula: Analytical Approximation Cable # [m] Cable # 1 0 [m] Cable # [m] [m] 1.3 [m] [m] Conductor Insulator 1 Sheath Insulator 2 Conductor Insulator 1 Sheath Insulator 2 Conductor Insulator 1 Sheath Insulator 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 d 2,3, which is calculated as: d2,3 d1 2r r m (5.1) Whereas d 1 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 # Cable # Cable # 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 8 aluminium is2.810 m, and it is increased with formula (4.1). The formula is presented again: Where r 1 is the conductor radius and 2 2 r c c m A 1200 c A c is the cross-section area of the conductor. 51

52 Permittivity It is not possible to model the semiconducting layers directly. Using equation (4.2) the permittivity is found to be: r 2 ln ' r 1 i b ln a Where i is the relative permittivity of the insulation, which is formed by XLPE and has a value of 2.3; r 2 and r 1 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 mm 2. 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] A n r 2 (5.2) Where r is the radius of each copper wire, which is calculated as: A 95 r 0.55 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: r 2 r sh 3 2, 8 8 ' s, cu s, cu m (5.4) A 95 s Where r 3 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 mm 2 8 and an equivalent resistivity of 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 m and its area is calculated: 52

53 Al A r r (5.5) Where r 2 is the outer radius of the aluminium sheath and r 1 is the outer copper wire radius. Using equation (5.2): Al A r r mm (5.6) The equivalent resistivity of the coaxial conductor formed by the two sheaths is calculated as: Cross bonding A A Cu Al 8 eq Cu Al m ACu AAl ACu A (5.7) Al 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. Ua2 Ub2 Uc2 C1 01 S1 C2 S2 C3 S3 C 01 C1 01 S1 S2 S3 C2 C3 C1 02 S [H] C2 S [H] C3 S [H] C 02 C1 02 S1 S2 S3 C2 C3 C1 03 S [H] C2 S [H] C3 S [H] C 03 C1 03 S1 S2 S3 C2 C3 Ua1 Ub1 Uc1 Sa2 Sa1 Sb2 Sb1 Sc2 Sc1 Fig. 5.4 Simplified PSCAD modelling of the sheath with cross-bonding 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 km. The figure below shows the cross bonding of this cable. 53

54 C AB C BC C CD Ca1 Cb1 Cc1 Sa1 C1 AB S1 C2 S2 C3 S3 C1 AB S1 S2 S3 C2 C3 C1 BC S [H] C2 S [H] C3 S [H] C1 BC S1 S2 S3 C2 C3 C1 CD S [H] C2 S [H] C3 S [H] C1 CD S1 S2 S3 C2 C3 Ca2 Cb2 Cc2 Sa2 Sb1 Sb2 Sc1 Sc Submarine cable Figure 5.5 Cross bonding points for the 2.3 km land cable. This cable is modelled using the same approximations as for the land cable. Ground Resistivity: [ohm*m] Relative Ground Permeability: 1.0 Earth Return Formula: Analytical Approximation Cable # [mm] Cable # 1 0 [m] Cable # [mm] [m] 1.3 [m] [m] Conductor Insulator 1 Sheath Insulator 2 Conductor Insulator 1 Sheath Insulator 2 Conductor Insulator 1 Sheath Insulator [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] Fig. 5.6 Layout of the submarine cable. The depth of cables 2 and 3 it is found using equation (5.1): d2,3 d1 2r r m Cable x-y position Cable # Cable # Cable # Table 5.2 Laying positions of the cables. The corrected resistivity of the core is calculated with equation (4.1): 54

55 Voltage [kv] 2 2 r c c = m A 630 c The permittivity of the insulation is modified using equation (4.2): ln r ln r ' i b ln ln a The sheath it is modelled with a resistivity of 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 [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 Voltage receiving end touching trefoil pipe-type Time [s] Fig. 5.7 Receiving end voltage comparison between touching trefoil configuration and pipe type configuration. 55

56 Voltage [ kv ] 200 Voltage at the receiving end time [s] 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 Bcc tt = B cs, while in the pipe-type cable is Bcc pt = 8 B cs. Then a capacitor with a value C, calculated below, is connected in parallel to each phase (see fig 5.1). F C 7 Ccs m 10 l m F 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 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] 56

57 5.4.2 Short circuit impedance Fig. 5.9 Voltage configuration and signal parameters. The grid, including the two shunt reactors in Endrup is modelled as an equivalent impedance as the next figure shows. Rgrid Lgrid Vsource Cgrid Fig Equivalent grid impedance. In this case the grid capacitance is considered having a small value. Therefore, its 1 capacitive reactance is calculated as: X C j 2 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 This value is considered to be accurate as was measured in the room control and will be used throughout the project. 57

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 cun Zk,150 Rx jx y j S (5.8) Where U n 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] X r, U j (5.9) Q 80 X r, U j (5.10) Q 40 The equivalent reactance of the two reactors, connected in parallel, is calculated as: X r, eq X X r,80 r,40 X X r,80 r, j (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: Z X j j k,150 r, eq Zeq Rx jx y j Zk,150 X r, eq j j (5.12) Where k,150 Z is the equivalent impedance without the shunt reactors and X r, eq is the equivalent reactance of the shunt reactors. Then, the short circuit inductance for 50 Hz is: L f mh (5.13) In the next figure it is represented the equivalent grid built up in PSCAD: 58

59 Voltage [ kv ] A R=0 B C [ohm] [H] [ohm] [H] [ohm] [H] Fig 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. BRKA Timed Breaker Logic Open@t0 BRKB Timed Breaker Logic Open@t0 BRKC Timed Breaker Logic Open@t0 Fig 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 Voltage-Endrup Phase a Phase b Phase c Time [s] Fig 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. 59

60 The switched on is set up to 0.01 seconds for phase a. Phase c is switched on at s. Then, phase b it is switched on at s. The 3 3 switching on times is presented in the next table. Variable Setting Switch time phase a 0.01 s Switch time phase b s Switch time phase c s Breaker open resistance 1 MΩ Breaker closed resistance Ω Table 5.2 PSCAD settings for the main breaker at Endrup station. 5.6 Shunt reactor In Chapter 3 section 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 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. 60

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: 1 L 2 f U I 2 R 2 (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: 61

62 Fig Saturation characteristic of the shunt reactor. [56, pg 26] As it can be appreciated the shunt reactor is unsaturated until it reaches approximately 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] Ua Ub Uc #1 #2 #1 #2 m #1 #2 Fig Layout model shunt reactor. In the next figure the input parameters of the coupled wires are given. [22] 62

63 Fig 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] Z b 2 2 U (5.15) S 80 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. 63

64 Fig 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 Input parameters for the magnetic saturation. 64

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 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 m/s (speed of light) of the travelling wave through the smallest segment, the travelling time is calculated as: km 6 km 2310 s s. Therefore the time step is selected as 1 µs. Fig Project settings. 65

66 Voltage [ kv ] 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 Ferranti effect - Improved model Sending end Receiving end time [s] 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. 66

67 Voltage [ kv ] Voltage [ kv ] 150 Voltage receiving end pipe-type cable Time [s] Fig. 6.2 Voltage calculated at the receiving end using the equations from chapter Voltage at the receiving end time [s] 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

68 Current [A] 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 aa a cia i1 3 B B B multiplying, B a by a factor, f Yaa, as:. Thus, the way to increase the permittivity of the armour is B f B B (6.1) aa Yaa a cia i1 f Ycs V apeak [kv] 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 Current Comparison Core Armour Time [s] Fig. 6.4 Current comparison at the sending end between the core and the armour 68

69 Current [A] 3 x 10-4 Current on the armour 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 ss s cjsi j1 3 B B B factor, f Yss :. To increase the permittivity of the sheath, s B f B B 6. 2 ss Yss s cjsi j1 3 f Yss V apeak [kv] B is multiplying by a Table 6.2 Peak voltage values increasing the permittivity of the sheath. 69

70 Voltage [kv] 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. 4 3 Current at the sending end Core Sheath Time [s] 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. f Ycs V apeak [kv] Table 6.3 Peak voltage values changing the insulation properties. 70

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. 71

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. 72

73 Literature 1. Ea- Energianalyse. Online. Cited: Hornsrev. Online. Cited: Offshore Center. Online. Cited: Dong Energy. Online. Cited: F. Faria da Silva, W. Wiechowski, C. Leth Bak, U. Stella Gudmundsdottir. Full Scale Test on a 100km, 150kV AC Cable. CIGRÉ, Wiechowski and P. Børre Eriksen. Selected Studies on Offshore Wind Farm Cable Connections Challenges and Experience of the Danish TSO. IEEE, B. Gustavsen, J. A. Martinez, and D. Durbak. Parameter Determination for Modeling System Transients Part II: Insulated Cables. IEEE Transactions on Power Delivery, Vol. 20, No. 3, July Anders Eliasson, Emir Isabegovi. Modelling and Simulation of Transient Fault Response at Lillgrund Wind Farm when Subjected to Faults in the Connecting 130 kv Grid. 9. A. I. Ibrahim, H. W. Dommel. A Knowledge Base for Switching Surge Transients. Presented at the International Conference on Power Systems Transients (IPST 05) in Montreal, Canada on June 19-23, K. Matsuura. Calculation of the transmission capacity of long-distance EHV singlecore submarine cable systems. IEEPROC, Vol. 128, Pt. C, No. 6, November Summary of EIA Report. Horns Rev Offshore Wind Farm Environmental Impact Assessment. Maj Stefan G Johansson, Lars Liljestrand, Flemming Krogh, Johan Karlstrand, and Jutta Hanson. AC Cable solutions for Offshore Wind Energy. 13. Brugg Cables. High voltage XLPE cable systems, Technical user guide. 14. M.Pavlovsky, P. Bauer Delft. Cable Selection and Shunt Compensation for Offshore Windparks. 15. Thomas Worzyk. Submarine Power Cables Design, Installation, Repair, Environmental Aspects. 73

74 16. F. Faria da Silva, C. L. Bak, U. S. Gudmundsdottir, W. Wiechowski, M. R. Knardrupgård. Use of a Pre-Insertion Resistor to Minimize Zero-Missing Phenomenon and Switching Overvoltages. IEEE Filipe Faria da Silva, Claus Leth Bak, Unnur Stella Gudmundsdottir, Wojciech Wiechowski, Martin Randrup Knardrupgård. Methods to Minimize Zero-Missing Phenomenon. IEEE Transactions on Power Delivery, Vol. 25, No. 4, October Gavita Mugala, Roland Eriksson. Dependence of XLPE Insulated Power Cable Wave Propagation Characteristics on Design Parameters. IEEE Paul Wagenaars, Peter A.A.F. Wouters, Peter C.J.M. van der Wielen, E. Fred Steennis. Estimation of Transmission Line Parameters for Single-Core XLPE Cables International Conference on Condition Monitoring and Diagnosis, Beijing, China, April 21-24, G. K. Papagiannis, D. A. Tsiamitros, G. T. Andreou, D. P. Labridis, P. S. Dokopoulos. Earth Return Path Impedances of Underground Cables for the multi-layer case - A Finite Element approach. Paper accepted for presentation at 2003 IEEE Bologna Power Tech Conference, June 23th-26 th, Bologna,Italy. 21. Jakob Bærholm Glasdam, Angel Fernandez Sarabia, Michal Korejcik, Davind Llorente Garcia. Analysis of Overvoltage and Inrush Current During Cable Energization. Institute of Energy Technology, Aalborg Universitet (Denmark). Semester spring Christian F.Jensen. Studies of transient overvoltage at the Horns Rev 2 wind farm HVAC cable connection. Institute of Energy Technology, Aalborg Universitet(Denmark). Semester fall F. Faria da Silva, Claus L. Bak, Wojciech T. Wiechowski. Study of High Voltage AC Underground Cable Systems. Paper submitted to the PhD Seminar on Detailed Modelling and Validation of Electrical Components and Systems 2010 in Fredericia, Denmark, February 8th, Claus Leth Bak and Wojciech Wiechowski. Analysis and simulation of switching surge generation when disconnecting a combined 400 kv cable/overhead line with shunt reactor. 25. The Manitoba HVDC Research. EMTDC User Guide V4.2. s.l. : The Manitoba HVDC Research, F. Castellanos. J. R. Marti, Member. Full Frequency-Dependent Phase-Domain Transmission Line Model. IEEE Transactions on Power Systems, Vol. 12, No. 3, August

75 27. Claus Leth Bak, Haukur Baldursson, Abdoul M. Oumarou. Switching Overvoltages in 60 kv reactor compensated cable grid due to resonance after disconnection. 28. Branch of System Engineering Bonneville Power Administration Portland, Oregon, United States of America. Electro-Magnetic Transients Program (EMTP)Theory Book. 29. U. S. Gudmundsdottir, J. De Silva, C. L. Bak,, and W. Wiechowski. Double Layered Sheath in Accurate HV XLPE Cable Modelling. 30. U. S. Gudmundsdottir, C. L. Bak and W. T. Wiechowski. Modelling of long High Voltage AC Underground Cables. 31. Nexans. Horns Rev 2 Offshore Wind Farm Technical Description of 170 kv submarine Cable. 32. Lou van der Sluis. Transient in Power Systems. s.l. : John Wiley & Sons Ltd, ISBN Greenwood, Allan. Electrical Transients in Power Systems 2nd. ed. s.l. : John Wiley & Sons, Inc., ISBN Kuffel, E. High Voltage Engineering - Fundamentals 2nd ed. s.l. : Newnes, ISBN Roy Maclean. Electrical System Design for the Proposed One Giga-watt Beatrice Offshore Wind Farm. Faculty of Engineering University of Strathclyde(United Kingdom). September Luis H-Restrepo, Gladys Caicedo Delgado, Ferley Castro-Aranda. Modelos de línea de transmisión para transitorios electromagnéticos en sistemas de potencia. Revista Energía y Computación Vol. 16 No. 1 Junio de 2008 p J. R. Martí, T. C. Yu. zcable Model for Frequency Dependent Modelling of Cable Transmission Systems. 38. Muhamad Zalani Daud. Transient behavior modelling of underground high voltage cable systems. School of Electrical, Computer and Telecommunications Engineering. University of Wollongong (Australia) 7-July Tarik Abdulahovi. Analysis of High-Frequency Electrical Transients in Offshore Wind Parks. Department of Energy and Environment Division of Electric Power Engineering, Chalmers University of Technology Göteborg, Sweden Tyco electronics. Energy division. 75

76 41. Y. Baba, N. Tanabe, N. Nagaoka, and A. Ametani. Transient Analysis of a Cable With Low-Conducting Layers by a Finite-Difference Time-Domain Method. IEEE Transactions on Electromagnetic Compatibility, Vol. 46, No. 3, August Unnur Stella Gudmundsdottir. Slides from the Course of Fundamentals of Underground and Submarine Power Cables. Aalborg Universitet (Denmark). Semester fall Training Course Presented by the Manitoba HVDC Research Centre. Introduction to PSCAD and Applications. 44. Nexans kv High voltage underground power cables. XLPE Insulated Cables. 45. Bjørn Gustavsen. Panel Session on Data for Modelling System Transients Insulated Cables. 46. Tleis., Dr Abdul Nasser Dib. Power Systems Modelling and Faults Analysis. s.l. : Elsevier Ltd., ISBN-13: Unnur Stella Gudmundsdottir, Bjørn Gustavsen, Claus L. Bak, Wojciech Wiechowski, F. Faria da Silva. Field Test and Simulation of a 400 kv Crossbonded Cable System.IEEE PES Transactions on Power Delivery. 48. Unnur Stella Gudmundsdottir, Claus L. Bak, Wojciech Wiechowski, F. Faria da Silva Wave propagation and benchmark measurements for cable model validation. IEEE PES Transactions on Power Delivery. 49. U. S. Gudmundsdottir, IEEE, J. De Silva, C. L. Bak, W. Wiechowski. Double Layered Sheath in Accurate HV XLPE Cable Modelling. 50. H.M.J. De Silva, L.M. Wedepohl, A.M. Gole. A robust multi-conductor transmission line model to simulate EM transients in underground cables. Paper submitted to the International Conference on Power Systems Transients (IPST2009) in Kyoto, Japan June 3-6, Bjørn Gustavsen, Adam Semlyen. Simulation of Transmission Line Transients Using Vector Fitting and Modal Decomposition.IEE Transaction on Power Delivery, Vol. 13, April L. Marti. Simulation of Electromagnetic Transients in Underground Cables using the EMTP. IEE 2nd International Conference on Advances in Power System Control, Operation and Management, December 1993, Hong Kong. 53. Ibrahim, A. I. and Dommel, H. W. A Knowledge Base for Switching Surge Transients. 2005, Presented at the International Conference on Power Systems Transients. 76

77 54. U. S. Gudmundsdottir, C. L. Bak, W. Wiechowski. Modelling of long of long High Voltage AC cables in the Transmission Systems EMTDC/PSCAD calculations of Zseries and Yshunt. 55. Moore, G.F, Electric Cables Handbook (3rd Edition).s.l: Moore, G.F., 1997 Blackwell Publishing. ISBN Power transformers ABB AB. Blaabjerg Reaktor Instruktionsmanual.ABB, A. Ametani, A general formulation of impedance and admittance of cables. IEEE Transactions on Power Apparatus and Systems, Vol. PAS-99,No. 3 May/June

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 r ic 0 r oc r is r os r ia r oa 104 Table A-1 Different radius of each layer. The cable is electrically described by its series impedance and shunt admittance. 78