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2 Content 1 INTRODUCTION .............................................................................................................................4 1.1 G ENERAL OVERVIEW OF A POWER SYSTEM NETWORK .................................................................................... 4 1.2 T REND IN TRANSMISSION AND DISTRIBUTION NETWORK IN D ENMARK ............................................................... 4 1.3 E NERGIZATION OF HV CABLE NETWORK ...................................................................................................... 5 1.4 O VERVOLTAGES DURING CABLE ENERGIZATION ............................................................................................. 6 1.5 T HE GRID INFLUENCE ON THE SWITCHING SURGE ........................................................................................ 10 1.6 D EENERGIZATION OF THE CABLE .............................................................................................................. 10 1.7 I NRUSH CURRENT WHEN CONNECTING A CABLE TO AN ALREADY ENERGIZED CABLE GRID ..................................... 11 1.8 C ABLE REPRESENTATION ........................................................................................................................ 13 2 PROBLEM ANALYSIS ..................................................................................................................... 15 2.1 P ROBLEM STATEMENT ........................................................................................................................... 15 2.2 A IM OF THE PROJECT ............................................................................................................................. 16 2.3 S OLUTION METHOD .............................................................................................................................. 16 2.4 L IMITATIONS ....................................................................................................................................... 16 2.5 A CKNOWLEDGEMENTS .......................................................................................................................... 17 3 DESCRIPTION OF HV CABLES .................................................................................................... 18 3.1 C ABLE TYPES FOR USE AT HV .................................................................................................................. 18 3.2 D ESCRIBTION OF XLPE INSULATED CABLES ................................................................................................ 18 3.3 E ARTHING METHODS , INDUCED VOLTAGES ................................................................................................ 20 4 SYSTEM DESCRIPTION .................................................................................................................. 23 4.1 S YSTEM DESCRIPTION ............................................................................................................................ 23 5 DESCRIPTION OF THE PSCAD MODEL ........................................................................................... 27 5.1 PSCAD MODEL SELECTION .................................................................................................................... 27 5.2 B UILDING THE MODEL IN PSCAD ............................................................................................................ 27 5.3 M ODELLING OF THE EQUIVALENT GRID ..................................................................................................... 33 5.4 T HE TIME STEP SIZE ............................................................................................................................... 34 5.5 M ODEL OF THE GRID ............................................................................................................................. 35 5.6 C HAPTER SUMMARIZATION .................................................................................................................... 35 6 RESONANCE FREQUENCY CALCULATION ...................................................................................... 36 6.1 C ALCULATION OF RESONANCE FREQUENCIES .............................................................................................. 36 6.2 P HYSICAL INTERPRETATION OF RESONANCE FREQUENCIES ............................................................................. 37 3 6.3 R ESONANCE FREQUENCY CALCULATIONS ................................................................................................... 40 6.4 R ESONANCE FREQUENCIES OBTAINED BY USING EQUIVALENT Π MODEL .......................................................... 41 6.5 C OMPARION BETWEEN METHODS ............................................................................................................ 44 6.6 C HAPTER SUMMARIZATION .................................................................................................................... 44 7 DESCRIPTION OF ENERGIZATION MEASUREMENT ....................................................................... 46 7.1 D ESCRIPTION OF THE SYSTEM .................................................................................................................. 46 7.2 D ESCRIPTION OF THE WORK DONE AT THE SUBSTATIONS .............................................................................. 48 7.3 T HE MEASUREMENTS ............................................................................................................................ 54 8 PSCAD MODEL VALIDATION AND ANALYSIS................................................................................. 55 8.1 M EASURING CONDITIONS AND CONSIDERATIONS ........................................................................................ 55 8.2 E NERGIZATION OF THE CABLE .................................................................................................................. 56 8.3 D E - ENERGIZATION ................................................................................................................................ 69 8.4 D ISCUSSION PSCAD MODEL .................................................................................................................. 76 8.5 W ORST CASE OVERVOLTAGES AND INRUSH CURRENT ANALYSIS ...................................................................... 84 8.6 V ELOCITY OF THE TRAVELLING WAVE ........................................................................................................ 87 8.7 C HAPTER SUMMARIZATION .................................................................................................................... 88 9 MINIMISATION OF THE SWITCHING OVERVOLTAGE .................................................................... 89 9.1 B ACKGROUND FOR OVERVOLTAGE MINIMISATION ....................................................................................... 89 9.2 P RE - INSERTION RESISTOR ....................................................................................................................... 90 9.3 S YNCHRONOUS CLOSING OF CIRCUIT BREAKER ............................................................................................ 94 9.4 C HAPTER SUMMARIZATION .................................................................................................................... 97 10 CONCLUSION ............................................................................................................................. 98 10.1 F UTURE WORK ................................................................................................................................. 100 11 LITERATURE ............................................................................................................................. 101 A APPENDIX CABLE PARAMETER CALCULATIONS ........................................................................ 104 Chapter 1 Introduction 4 1 Introduction In this chapter will be described the basics of the phenomena occurring during energization of a cable. 1.1 General overview of a power system network The generated power from power plants, wind farms, etc. is transported and distributed to the consumers using the electrical grid, which is formed by the transmission and distribution systems depending on the voltage levels. At transmission level the grid is dominantly laid out as overhead lines, where as the distribution mainly consist of underground cables. In Denmark the transmission network is operated by TSO (Transmission System Operator) Energinet.dk A/S at 400 kV, 220 kV, 150 kV and 132 kV. The Danish distribution network is operated by local DSO (Distribution SO) and the levels are 60 kV, 10 kV 0,4 kV.(1) There has to be a balance between the power generated, transmitted and consumed by the customers, since energy cannot be stored in large quantities. Furthermore, the frequency and voltage of the system has to be held constant. 1.2 Trend in transmission and distribution network in Denmark In 2008 it was decided in Denmark that all voltage levels up to 400 kV will within the next 20 years be put in the ground. There is no long time experience with long high voltage AC (HVAC) cables and the longest is located in Tokyo and is 40 km long. The main reasons for replacing overhead lines (OHL) by cables in Denmark are that people were protesting against the OHL in order to sustain and protect the environment. (2) 1.2.1 Advantages and disadvantages of using cables compared with overhead lines In chapter 3 a more detailed description of cable characteristics is given. At this point some of the advantages and disadvantages of using cables compared with overhead lines are given: Chapter 1 Introduction 5 Advantages: (3) • Cables occupy much less free space, since they are located in the ground • The risk of electric shock is less • Cables are less exposed to suffer damages caused by storms, lightning etc. • The risk of corrosion is less Disadvantages: • The investment costs for cables are higher but the cost of high voltage cables and accessories is decreasing • Repair is more difficult than OHL • There exist no long time experience with long high voltage cables • The location of an occurring fault is more difficult to detect • The capacitance is much higher (20-50 times (4)) which usually has to be compensated by the use of shunt reactors • By using shunt reactors, resonance frequencies between the reactor and the cables capacitance is approximately 45-47, which is very close to the operation frequency. (5) • Since the losses (and hence the resistance) in a power system is low, transient oscillations caused by for example a switching operation is low damped. During this prolonged oscillation dangerously high voltages may occur. (5) • Same life time as OHL (40 years), but the OHL can be renovated, yielding a prolonged life. (6) 1.3 Energization of HV cable network One of the problems associated with the use of cables at transmission as well distribution levels are cable energization. As will be described in chapter 2 the aim of this report is to investigate the transient behaviour of a cable when it is being energized as well as being de-energized. The fundamental of the transient phenomena during an energization of a cable integrated in a cable network will be described in the following. Chapter 1 Introduction 6 1.3.1 Problems associated with energization of a HV cable • Resonance circuits Cables consist of a large shunt capacitance and some series impedance forming various resonance circuits so that there will be energy oscillation between the electric and magnetic field at certain resonance frequencies during energization which can cause overvoltages. • High overvoltage at the receiving end of the cable during energization compared with the sending end due to reflections • De-energization of the cable When the cable is being disconnected some trapped energy stores in the electric field, which can cause a high voltage across the circuit breakers contacts. • High inrush current from the already energized cables connected at the same busbar When energizing a cable located in a cable grid, an energy transfer from the already energized cable to the switched on cable takes place. The above mentioned phenomena will be described in the following. 1.4 Overvoltages during cable energization A transient overvoltage can occur when a cable is being energized. The amplitude depends on the instant value of the phase voltage when the circuit breaker is closed at t 0 . The maximum overvoltage will occur if the grid voltage is at its peak value at t 0 . If the voltage is crossing zero at t 0 the transient overvoltage will be at its minimum. This is caused by the charging of the cables capacitances and an energy exchange between the electric and magnetic field will begin. In order to explain the overvoltage a very simplified single-phase model of the cable under investigation is represented by a lumped LC circuit in PSCAD with open end. The parameters are calculated in chapter 6 and appendix A. Chapter 1 Introduction 7 In chapter 4 a description of the system is made. The system voltage is 61,5 kV given by Magnus L. Hansen ENV A/S. In fig 1-1 are shown the PSCAD model and simulation results. fig 1-1 Voltages and current in LC circuit during the energization of a lossless cable. Parameters: L = 166,83 µH/km, C = 185 nF/km, cable length: l = 11,94 km Note: Current is off-scale, multiplied by 20 The natural frequency of the oscillating current is: 0 1 1 2,4 22 11,94 166,83 185 km km f kHz L l C l H nF km km km π µ π = = = ⋅ ⋅ ⋅ ⋅ ⋅ (1.1) and the value of the peak current is: Chapter 1 Introduction 8 ,1 ,1 0 61,5 2 23 1,67 166,83 185 peak f RMS f peak km km kV U U I kA ZL H km CnF km µ ⋅ = = = = (1.2) In the simulation the switching occurs when the source voltage is at its peak value at t o . From the moment of switching, the capacitor is charged by the current, which is flowing through the inductance. The oscillation between magnetic and electric energy begins. At t 1 the voltage across the capacitor, U c is the same as the source U s , so the current reaches its peak value. After t 1 U c is higher than U s and because current in the inductance cannot change instantly, so the current is still positive and going towards zero. Until the current crosses zero at t 2 U c is still being charged. At t 2 U c is equal to 2U s,peak . In fig 1-1 the natural frequency f 0 is much higher than the source frequency (50 Hz). This means that the value of the U s is almost the same between two consecutive intersections between U S and U c (indicated by the red line). If f 0 is decreased (for example if the cable length is increased see eq(1.1) U s will match U c for different points so the value of U c will change for each cycle. In order to see this one should refer to (7). In the above resistance has been neglected. A real cable has some series resistance, which damps the oscillations. 1.4.1 Receiving end overvoltage During energization the circuit breaker in the receiving end is left open. Because of the charging current of the cables capacitances 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. (4) This phenomenon is called Ferranti Effect and can be explained by use of the nominal π model shown in fig 1-2. By drawing the corresponding phasor relationships as shown in fig 1-3 it can be seen that the magnitude of the receiving end voltage is higher than the sending end. Chapter 1 Introduction 9 fig 1-2 Nominal π model fig 1-3 Phasor relationship for the nominal π model The voltage in the receiving end can be found on basis of fig 1-2. The capacitance in the sending end has no influence on the voltage drop along the cable. U r is thus: 2 22 2 22 1 1 c C r s s s C c series C j Z U U U U Z Z j j L L ϖ ϖ ϖ ϖ − = = = + − + − (1.3) In the above equation the voltage drop on the series resistance is neglected so it will only give information of the magnitude difference. (4) The Ferranti effect for steady state (50 Hz) is calculated: ( ) ( ) 2 2 2185 22 1 1 11 2 50 166,83 11,94 nF km r s s CHkm U U U Lkm µ ϖπ = = −− ⋅ ⋅ ⋅ ⋅ (1.4) 4 1 1 2,17 10 r s s U U U − =− ⋅ ≃ (1.5) So the Ferranti effect is not present under normal operation. Chapter 1 Introduction 10 1.5 The grid influence on the switching surge In this section the grids influence on the switching transient is described. The grid can be classified as being strong/stiff or weak. For a strong grid its short circuit power is infinite and the source´s equivalent grid impedance Z grid is zero (4). In fig 1-4 two cables are connected where cable 1 is in service and cable 2 is not. fig 1-4 Energization of a cable when connecting to a busbar where an in-service cable is connected The impedance when looking into the cable from the switch S when it closes is Z cable = Z 0 (characteristic impedance of the cable). Z grid1 is formed by the grid impedance in parallel with the impedance of cable 1. By voltage division the voltage across the cable is: 1 o cable s o grid Z U U Z Z =+ (1.6) For a strong grid Z 0 >> Z grid1 which implies that the voltage surge will be on the cable. If the grid is weak the grid will absorb a fraction of the travelling surge. 1.6 Deenergization of the cable When the cable is being switched off (de-energized) a transient occurs. Since a cable is mainly a capacitive element, the current leads the voltage by 90°. Switching devices are Chapter 2 Problem analysis 17 Measurements are also made when the cable is being de-energized. In order to compare simulation and measurement this would imply modelling of the measurement transformers since saturation of the transformer core occurs. However the needed data were not available, so the transformers will not be modelled. This is justified by the fact that the main aim of the project is the investigation of the transient during energization. For the field measurement the following limitations are made since they are both time consuming and the available time for the field measurement where limited: • No measurement of the travelling time of the switching surge will be made The used measuring equipment, Omicron 256, can be equipped with a GPS transmitter, so that the travelling time can be obtained with high accuracy. The measured travelling time could have been used as a part of the PSCAD model validation • No resonance frequency measurement One of the projects main parts is the calculation of the resonance frequencies causing the transients. The measurement of the resonance frequencies could be made by doing a frequency sweep using an AC generator with variable frequency. The measured frequencies could have been used as a part of the PSCAD model validation. 2.5 Acknowledgements The project group would like to give acknowledgements to ENV A/S for letting the group perform switching actions in its network. A special thank is given to engineer Magnus L. Hansen for providing necessary information. Chapter 3 Description of HV cables 18 3 Description of HV cables In this chapter a description of HV cables is given. The most commonly used type the cross linked polyethylene cables (XLPE) will be described in more detailed. A brief description of grounding methods in order to limit the induced voltage on the cable screen is given. 3.1 Cable types for use at HV There exist four main cable types, which are briefly explained: (11) • Oil impregnated paper cables Before the development of XLPE cables in the late 1950´ies, oil impregnated paper was the only reliable insulation for HV cables. The conductor is wound with paper, so that the insulation consists of 50 % paper and 50 % air. In order to have the highest homogeneity as possible, the paper is oil impregnated. • Extruded polymer cables (XLPE) Solid polymers have the property of being extrudable, which makes the manufacturing less complicate and expensive. XLPE is the most widely used insulation in cable systems. (12) • Gas insulated systems (GIS) GIS are closed systems, where the inner conductor is held in a cylindrical outer conductor. GIS is often used to connect busbars, bushings and breakers. The insulation is SF 6 . • Superconducting cables Are under development 3.2 Describtion of XLPE insulated cables The most used insulation type is the cross linked polyethylene cables (XLPE), which has its origin in the late 1950´ties. The initial cost of the cables and installation at that time was much higher than overhead lines (OHL), but the difference started to decrease in the 1980´ties. (13) The cost for cables are still high compared to OHL. Chapter 3 Description of HV cables 19 XLPE insulated cables have a low permittivity, low losses, high dielectric strength and low thermal resistivity in order to prevent overheating of the conductor. As explained in the following the XLPE insulation is thermosetting. (11) 3.2.1 Polymers Polymers can be divided in thermoplastic (PE, polyethylene) and thermosetting materials (XLPE or PEX, cross linked polyethylene). The molecules in thermoplastic materials are linked by weak bonds, that can be broken if the temperature is increased. This makes the insulation flexible and there is a risk that the conductor will move from its original position. By chemically cross linking the polymer chains the material becomes thermosetting, which means that the hardness of the insulation does not change by heating. (11) 3.2.2 Considerations for use of XLPE insulation XLPE cables are not self healing and are not able to resist partial discharges, so the following measures must be taken in order to sustain control of the electric field: (11) • Pure and homogeneous material The insulation should contain very few impurities and gas filled voids, which can cause a local electric field enhancement. This can ultimately cause partial discharges and electrical treeing, which is a small conducting channel see fig 3-1. • Water proof sheath If water penetrates the sheath and enter the insulation, water treeing might occur, see fig 3-1. fig 3-1 Electric treeing in cable insulation caused by appearance of water. a) Conducting channels caused by water. b) Field enhancement causing electric tree. c) Final breakdown Chapter 3 Description of HV cables 20 The water trees themselves are not dangerous, but can create small conducting channels which can lead to an increase in the field strength, which again can lead to electrical treeing and create a breakdown of the insulation. • Good connection between inner screen and conductor In order to secure a homogeneous field distribution an inner screen is inserted (field limiting layer), which is in good contact with the insulation, see fig 3-2. fig 3-2 Electric field line distribution in cable insulation (cross section). a) No inner screen. b) inner screen with good contact to the conductor The best way to make a good connection is to choose the material of the inner screen similar to the insulation material. 3.3 Earthing methods, induced voltages Since the cable screen is conductive, voltages will be induced along the cable caused by the conductor current in the three phases and parallel lines, if present. An overview of some of the measures to limit the induced voltage is given in table 3-1. (13) table 3-1 Overview of grounding methods for cables Grounding method Standing 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 Chapter 3 Description of HV cables 21 A description of single-end and both-end grounding method are presented in the following. 3.3.1 Single point grounding By grounding in only place, the voltage will increase linearly with distance to the grounding point as shown in fig 3-3. In order to avoid dangerously high voltage at end of the cable, voltage limiters should be inserted (not shown in the figure). (12) fig 3-3 Single point ground and screen voltage profile along cable. a) end point ground. b)midpoint grounding 3.3.2 Both end or multiple grounding In fig 3-4 a setup with both ends grounded is shown. fig 3-4 Both end grounding creating a complete screen ground path for the induced current By grounding in this manner, or using several grounding points along the cable, the induced voltage will be limited. However, since a closed loop is made, the induced voltage induces current to flow in the screen and ground. These induced circulating Chapter 3 Description of HV cables 22 currents are proportional to the conductor current and reduces the overall ampacity of the cable as well as increasing the temperature. From a safety point of view this method is the most secure available. From an economical aspect this is the most disadvantageous method. (13)(12) The cable under investigation is grounded at both ends. Cross bonding grounding is not used since no joints are required due to the short length of the cable (according to table 3-1 therefore falls under the category “short cables“). Chapter 4 System description 23 4 System description In this chapter a description of ENV´s 60 kV network is made. 4.1 System description The cable that is going to be energized in simulation as well as in field measurement is located in ENV Net A/S 60 kV distribution grid in Northern Jutland as shown in fig 4-1. A larger map of ENV´s network is provided on the CD. fig 4-1Map of Denmark (from google maps) and the 60 kV ENV A/S network The cable being energized is located in the Starbakke grid, which is currently formed by two separate loops (14). The relevant cable is located in the loop, which is going from Starbakke to Hedebo and back (a one line diagram is provided on the CD), and is connecting the substations in Ålbæk (ÅBK) and Måstrup (MSP). The cable energization will be made in ÅBK (sending end). The circuit breaker in the receiving end in MSP is left open. In fig 4-2 a part of Starbakke grid is shown. The solid lines indicate that the cable is implemented in the PSCAD model. Chapter 4 System description 24 fig 4-2Part of Starbakke grid The grid is supplied in Starbakke through two 100MVA transformers. In the part of Starbakke grid are situated the cables shown in table 4-1. Chapter 4 System description 25 table 4-1 Cables in Starbakke grid (14) No. Section Type Length [km] Soil B13 MSP – SDL 400mm 2 PEX-M-AL-LT 72kV 150mm 2 PEX-CU 2,727 3,800 Clay / Mull Clay / Mull B14 MSP – ÅBK 400mm 2 PEX-M-AL-LT 72kV 11,940 Clay / Mull / Sand B15 ÅBK – HDB 400mm 2 PEX-M-AL-LT 72kV 18,511 Sand B16 ÅBK – HDB 400mm 2 PEX-M-AL-LT 72kV 18,934 Sand B18 SBA – MSP 400mm 2 PEX-M-AL-LT 72kV 13,360 Clay / Mull B23 HDB – ØRB 50mm2 Flat cable 2,680 Sand B37 HDB – ØRB 150mm 2 PEX-CU 3,150 Sand B44 SBA – STD 240mm 2 PEX-M-AL-LT 72kV 4,600 Clay / Mull / Sand B45/ B46 STD – ÅBK 240mm 2 PEX-M-AL-LT 72kV 16,000 Clay / Mull / Sand B55 HDB – NDB 400mm 2 PEX-M-AL-LT 72kV 2,209 Clay / Mull / Sand The examined cable system B14 consists of 3 x 1 phase PEX-M-AL-LT 72kV cables, which are manufactured by NKT. The cross section of the conductor is 400 mm 2 . The length of the cable is 11,940 km. The cable system lies 1,3 m under the surface in a close trefoil layout as shown in fig 4-3. The ground consists of clay, mull and sand. The resistivity of the surrounding ground depends of many factors (humidity etc.) and is determined as 100 Ωm, since it is the default value in PSCAD. Chapter 4 System description 26 fig 4-3 Cable close trefoil layout All the relevant cable parameters for PSCAD are given in section 5.2. The sheath is grounded in both end of the cable. The reason for this is explained in chapter 3. Chapter 5 Description of the PSCAD model 33 5.3 Modelling of the equivalent grid In order to include the grid in the model it will be modeled as an equivalent impedance as shown in fig 5-3. fig 5-3 Equivalent grid model Data for the short circuit power in the feeding point in Starbakke (refer to fig 4-2) is given by Magnus L. Hansen and can be found on the CD. The maximum and minimum short circuit power S k ” is given as 1061,91 MVA and 541,25 MVA respectively. In order to take into loads a factor c is used to correct the voltage at the fault location before the fault occurs. (4) The value of c for the minimum and maximum short circuit calculation is 0,9 and 1,1 respectively. (see the table on the CD). In table 5-6 are shown the calculated parameters for the equivalent grid. A value between the maximum and minimum short circuit power is chosen to be " 800 83,5 k S MVA = ∠−  , which is assumed to be a representative of the grid during the measurement. This value will be used throughout the report. table 5-6 Equivalent grid parameters Short circuit power S [MVA] φ [º] c [-] grid Z [Ω] R [Ω] X [Ω] Min 541,25 -82,55 0,99 6,86 0,8897 6,8041 Normal 800,00 -83,50 1,10 5,16 0,5839 5,1252 Max 1061,91 -84,28 1,10 3,89 0,3873 3,8668 Chapter 5 Description of the PSCAD model 34 In (7) a standard value of the grid capacitance is given as C grid =2nF. X c will thus yield a very high number and will act as an open circuit in fig 5-3 so it can be neglected in the following calculation of the reactance. It will be implemented in PSCAD with 2nF. The grid impedance for " 800 83,5 k S MVA = ∠−  is calculated as: ( ) 2 2 " 61,25 1,1 5,16 83,5 800 83,5 n grid k kV U Z R jX c S MVA ϕ = + = = = ∠ Ω ∠ ∠−  (5.3) The real part of Z grid is: ( ) 0,5839 grid grid R real Z = = Ω (5.4) The imaginary of part Z grid is then : ( ) 5,1252 grid L X X imag Z = = = Ω (5.5) The equivalent inductance of the grid for 50 Hz can be found: 5,1252 16,3140 2 50 L grid X L mH ω π = = = ⋅ ⋅ (5.6) 5.4 The time step size An appropriate time step value must be chosen in the Project Settings of PSCAD. If the time step is too high, the simulation can be distorted, but on the other hand a too small time step could be time-consuming. An ordinary adjustment of the time step size is for switching transients between 10µs to 100µs, where it is assumed that the highest frequency during switching is 10 kHz. (17) A good rule is the following (18): “If you want to check the accuracy of the simulation, then divide the used step size by 2 and run the simulation.” If the result for the new simulation does not differ significantly the time step is valid. For all simulations is used the time step ∆ t = 30 µs since it is close to the time step of the omicron: Chapter 5 Description of the PSCAD model 35 samp 1 1 t= =35,7 s f 28 µ kHz ∆ = (5.7) where f samp is the highest sampling frequency of omicron. A simulation with ∆t = 15 µs has been made which gave the same result as ∆t = 30 µs, so the chosen time step is appropriate. 5.5 Model of the grid In fig 5-4 is depicted a part of the Starbakke loop, which consist of a feeder (with grid impedance), cables, two circuit breakers (on each end of cable B14). fig 5-4PSCAD model of part of Starbakke loop 5.6 Chapter summarization In this chapter a brief explanation of the model developed in PSCAD has been made. The model will be validated in chapter 8 where simulations will be compared with field measurements. The PSCAD model can be found on the CD. Chapter 6 Resonance frequency calculation 36 6 Resonance frequency calculation In this chapter the resonance frequencies causing the overvoltage during energization will be calculated. This is done firstly by an analytic approach based on the theory of standing waves. The resonance frequencies will also be found using the equivalent π model implemented in Matlab. The two methods will be held against a frequency plot of the PSCAD model developed in the previous chapter. 6.1 Calculation of resonance frequencies When a cable is being energized by closing the circuit breaker a switching wave will travel down the cable. The travelling wave contains a wide spectrum of frequencies superimposed on the 50 Hz signal. For each of these frequencies a physical length is associated (the signals wavelength) and is given as: (19) v f λ = (6.1) Where λ is the wavelength, f is the frequency and v is the velocity of the wave. As it can be seen, the wavelength is inversely proportional to the frequency, meaning that the wavelength decreases as the frequency increases. The velocity can be calculated as: (10) 1 v L C = ⋅ (6.2) The wavelength is the distance between two following peaks of a signal. In the following it will be explained why at specific wavelengths resonance will occur. For certain frequencies the wavelength will correspond to an odd multiple of the quarter of the cable length (λ = ¼·Length, ¾·Length, 1¼·Length etc). For other frequencies the wavelength will correspond to half the length of the cable (λ = ½·Length, 1·Length, 1½·Length etc). This is visualised later in fig 6-2 and fig 6-3, but first an explanation of the matter. Chapter 6 Resonance frequency calculation 37 In order to find the resonance frequencies for the cable, the input impedance Z in for the cable terminated with the load impedance Z L is given as: (20) ( ) ( ) 0 0 0 tan tan L in L Z j Z l Z Z Z j Z l β β + ⋅ ⋅ = ⋅ + ⋅ ⋅ (6.3) Where Z0 is the characteristic impedance of the cable, β is the phase constant in rad/m and l is the length of the cable. In equation (6.3) it is assumed that the cable is lossless. When the cable is being energized the receiving end will be left open so that ZL = ∞ Ω . In fig 6-1 tan( βl ) is plotted as function of l . fig 6-1 Tangents as function of length If λ is set equal to the length of the cable, l = λ , it can be seen from fig 6-1 that tan( βl ) approaches infinity for frequencies where the odd multiple of the quarter wavelength corresponds to the cable length. It can also be seen from fig 6-1 that tan( βl ) = 0 for signals with a frequency, where the corresponding wavelength is equal to the multiple of half the cable length. 6.2 Physical interpretation of resonance frequencies The physical interpretation of resonance frequencies will be explained on basis of standing waves which is explained in (21). Chapter 6 Resonance frequency calculation 38 Standing waves are formed by two signals with the same frequency travelling in opposite direction along the cable. The sum of the two waves results in a stationary waveform. (21). In fig 6-2 voltage and current waveforms for quarter wave frequencies are shown. As will be shown in the following, the load impedance at these frequencies is inversely transferred to the input. Hence for open circuit the voltage is zero (a so called node) and the current is at max (antinode). In fig 6-3 voltage and current waveforms for half wave frequencies are shown. As will be shown in the following, the load impedance at these frequencies is directly transferred to the input. Hence for open circuit the voltage is at an antinode and the current is at a node. When standing at the end of the cable (x = l) and looking into the terminal the impedance is theoretically infinitive, which explains why the voltages are at an antinode and currents are at a node for both quarter and half wave frequencies. fig 6-2 Standing voltage and current waveforms for odd multiple of ¼ wavelengths of an open circuited cable with the length l. The waveforms are copied from (21) fig 6-3 Standing voltage and current waveforms for multiple of ½ wavelengths of an open circuited cable with the length l. The waveforms are copied from (21) Chapter 6 Resonance frequency calculation 39 Attending to equation (6.3), Z in for frequencies where the corresponding wavelength is either a multiple of half or an odd multiple of the quarter wavelength will be analysed in the following. • Quarter wavelength (l = ¼ λ, ¾λ, 1¼ λ etc) This case is valid when the quarter of the wavelength λ is an odd multiple of the cable length, l. As described in the above, tan(βl) approaches infinity at λ/4. Equation (6.3) can thus be simplified: 2 0 0 0 0 L in L L Z j Z Z Z Z Z j Z Z + ⋅ ⋅∞ = ⋅ = + ⋅ ⋅∞ (6.4) This means, that for frequencies with a wavelength of odd multiple of the cable length, the inverse of the load impedance is transferred to the input of the transmission line. So for open circuit the input impedance is zero. • Half-wave section ( l = ½λ, 1λ, 1½λ etc) Again returning to fig 6-1, tan(βl) = 0 for frequencies with integer multiple of half the wavelength equation (6.3) results in: 0 0 0 0 0 L in L L Z j Z Z Z Z Z j Z + ⋅ ⋅ = ⋅ = + ⋅ ⋅ (6.5) As it can be seen, for half wave frequency the impedance of the transmission line is missing. The Z in does not depend on the transmission line parameters so the load impedance is transferred directly to the input terminal. It is practically not possible to have infinite load impedance even if the cable is open ended. This is because of radiation from the open end and by coupling to nearby objects. (20) When the project group is energizing the cable B14 in Ålbæk, the receiving end in Måstrup is left open. The resonance frequencies will therefore have a wavelength that is Chapter 6 Resonance frequency calculation 40 a multiple of half the cable length. For example the cable is 11,94 km, so the resonance frequencies have wavelength of ½·11,94 km, 1·11,94 km, 1½·11,94 km and so forth. 6.3 Resonance frequency calculations The resonance frequencies of the cable can be calculated on basis of the above mentioned relationship between input impedance and wavelength. The parameters of the cable have been calculated in appendix A for 50 Hz and are shown in table 6-1. table 6-1 Parameters of the cable used in energization measurement Capacitance (nF/km) Inductance (µH/km) Resistance (Ω/km) Length (km) 185 188,63 0,0778 11,94 The velocity of the travelling wave is calculated from (6.2): 1 1 169281 188,63 185 km km km v s L C H nF km km µ = = = ⋅⋅ (6.6) In equation (6.6) is used the 50 Hz values for simplicity Now it is possible to calculate the resonance frequencies. For the frequency where the wavelength is equal to the length of the cable is calculated 169281 169281 11,94 14,2 11,94 l km km vs s km f kHz f f km λ λ = = = = ⇒= = (6.7) Generally the resonance frequencies can be calculated as: 169281 ; 0,5;1;1,5... 11,94 km vs f n l km nn = = = (6.8) In table 6-2 are shown the calculated resonance frequencies for n = [0,5 2]. Chapter 6 Resonance frequency calculation 41 table 6-2 Calculated resonance frequencies, for open termination where l is the length of the cable and λ is the wavelength of the signal Z in [Ω] n = 0,5 (l = ½λ) [kHz] n = 1 (l = 1λ) [kHz] n = 1,5 (l = 1½λ) [kHz] n = 2 (l = 2λ) [kHz] ∞ 7,1 14,2 21,3 28,4 6.4 Resonance frequencies obtained by using equivalent π ππ π model Another approach in calculating the resonance frequencies is by using the equivalent π model of the cable, which is described in (4) and (22). The equivalent π model of the cable terminated with Z load at the receiving end is shown in fig 6-4. fig 6-4 Equivalent π model of the cable Where: (4) ( )( ) 2 1 2 2 1 2 1 2 2 sinh( ) ( ) tanh( ) 2 2 2 2 tanh( ) ( ) ( ) ( ) ( ) series km km l km l l c c l km km km km km km km l Z R j L l l j C l Y Y Z Z j C l R j L l j C l l R j L j C j γ ωγ ωγ γ γ ω γ γ ω ω ω ω α β − ⋅ = + ⋅ ⋅ ⋅ ⋅⋅ = = ⋅ ⇒ ⋅   ⋅ = = − ⋅  ⋅ ⋅   = + ⋅ ⋅ = ⋅ + ⋅ = + (6.9) The input impedance in fig 6-4 is found: Chapter 6 Resonance frequency calculation 42 ( ) ( ) 1 2 2 1 2 2 1 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) in c series c load c load c series c load c load c series c load Z j Z j Z j Z j Z j Z j Z j Z j Z j Z j Z j Z j Z j Z j Z j Z j Z j ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω = +   ⋅ ⋅ +   +   =   ⋅ + +   +   (6.10) Since Z load = ∞ Ω equation (6.10) can be simplified: ( ) ( ) 1 2 1 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) c series c in c series c Z j Z j Z j Z j Z j Z j Z j ω ω ω ω ω ω ω ⋅ + =+ + (6.11) The absolute value of Zin is plotted against frequency (f = ω /(2 π )) in fig 6-5, where skin effect is included, as described in appendix A. In the figure is also plotted the PSCAD simulated resonance frequencies of the cable. The m-file of the equivalent π model can be found on the CD. fig 6-5 Resonance frequencies using the PSCAD model and by using the equivalent π model. From fig 6-5 it can be seen that the resonance peaks at low frequency is somewhat the same for the equivalent π model as for the PSCAD model. The frequency shift becomes higher when the frequency is increased. It can also be seen that the amplitude is higher for π model. The proportion of the decay of the amplitude versus frequency is the same and is the upper asymptote is Z0 · tanh( √ (Y · Z)) where the characteristic impedance is Z0 = √ (Z/Y). (23) Chapter 7 Description of energization measurement 49 As can be seen from fig 7-2 the measuring transformers are located on the cable side of the circuit breaker in both stations. So in order to see the voltage before and after the switching, the voltage at one of the other fields in ABK is measured from the protection circuit located in the same cabinet as the cable to MSP. The advantage of the measuring transformers location on the cable side of the circuit breaker is that it is possible to measure the voltage directly in MSP, without any need of inserting voltage dividing equipment. 7.2.1 Setting up the measuring equipment Firstly the recognizing of the terminals is performed by looking at the schemes of each cabin. The terminals can be seen in fig 7-3. fig 7-3 The terminals of the protection circuit in the cabinet, where the Omicron will be connected The terminals of the protection circuit in the cabinet are connected to the Omicron according to the configuration of the software. The omicron is connected to a laptop in order to access the measurements. In fig 7-4 a scheme of the set up is shown. Chapter 7 Description of energization measurement 50 fig 7-4 Measuring setup It was noted during inspection that the current transformer is measuring the current of the whole cable (conductor and sheath). This implies that the measurement is a result of the sum of core and sheath currents if no countermeasure is done. In fig 7-5 it can be seen how the sheath effect is eliminated by letting the sheath conductor pass the current transformer two times. Chapter 7 Description of energization measurement 51 7.2.2 List of used measuring equipment In table 7-1 are listed the used measuring equipment. table 7-1 List of used measuring equipment Equipment Quantity Omicron CMC 256-6 2 Currents probes LEM PR30 3 Voltage Probe Tektronix 1 Limitation of the equipment The current probes have a sensitivity of 100 mV/A and an overload capability of 500 A. The current transformer ratio is 500/5 A. So the upper limit is a peak of current of 50 fig 7-5 Scheme of current transformer Chapter 7 Description of energization measurement 52 kA in the cable, which is much higher than the simulated inrush current of 1,218 kA for worst case simulation (see section 8.5). The upper limit of voltage input for the omicron is 0,6 kV between the input terminals. The voltage transformer has a ratio of 60 / 0,1 kV. It is by far not expected to reach the upper limit of the omicron (corresponds to a peak of 360 kV on the primary side). 7.2.3 ABK Substation set up At the substation the three voltage terminals of the protection circuit are connected directly to the positive terminals of input port 1, 2 and 3 of the omicron. The ground of the voltage outlet in the cabinet is connected to the ground of the ports 1, 2 and 3 in the omicron. In order to limit unwanted noise a ground wire is twisted for each phase. Finally these grounds are short circuited. The chassis of the omicron is grounded to the chassis of the cabinet. fig 7-6 Connection of the protection circuit and the omicron Direct current measurements are not possible in the Omicron because of the input only measures voltages. For measure the corresponding currents for each phase current probes are used as shown in fig 7-7. Chapter 7 Description of energization measurement 53 fig 7-7 Setup for current measurements The output of the current clamp is a voltage and is connected to terminal 5, 6 and 7 of the omicron. In order to trigger the omicron a 230 VDC impulse outtake of the cabinet is connected to input 4 of the omicron as shown in fig 7-4 Measuring setup. A voltage probe is used to separate the DC ground and the AC ground. 7.2.4 MSP substation set up At MSP the three voltage terminals of the cabin are connected directly to the input ports 1, 2 and 3 of the omicron, and have mutual ground, see fig 7-8. The chassis of the omicron is grounded to the chassis of the cabinet. Chapter 7 Description of energization measurement 54 fig 7-8 Måstrup substation set up Since there is no triggering impulse the omicron is triggered by the incoming voltages. The omicron is capable of acquiring data the instant before the triggering event (pretriggering). The trigger is done by programming the trigger of the omicron with a voltage rising in one phase of 50 V and pre-trigger time of 0,5 seconds. 7.3 The measurements The test consists of six switching measurements, three for energization and three for deenergization. The highest sampling frequency of the omicron is used in order to have the best resolution of the plots (28 kHz for 11,7 s duration (including pre-triggering)). The measurement results will be presented, analysed and compared with simulation results in the following chapter. Chapter 8 PSCAD model validation and analysis 55 8 PSCAD model validation and analysis In this chapter PSCAD simulation and measuring results of cable energization and deenergization are presented and compared. This is done on basis of the developed PSCAD model described in chapter 5. A description of the field measurement can be found in chapter 7. On basis of a comparison between measurements and simulations the PSCAD model will be evaluated as an appropriate tool to predict the switching transients and to design and test solutions for minimizing the transient voltage and current in chapter 9. 8.1 Measuring conditions and considerations As explained in chapter 7, the voltage is measured at three locations: At the cable side of the circuit breaker in the substations in Ålbæk (ABK, sending end) and Måstrup (MST, receiving end). The grid voltage is also measured by using one of the voltage transformers located in one of the adjacent fields in ABK. The grid measurement is done in order to see the switching impact on the grid as well as the condition at the instant of switching. The input voltage in PSCAD will be adjusted so it is the same as the measured. The phase currents are measured in the sending end of the cable in ABK. The circuit breaker in MST is kept open during the measurements. The closing / opening of the circuit breaker is not synchronized, which implies that the three phases are ideally connected / disconnected at the same instant. During the studying of the measurement it became evident, that the circuit breaker has a delay time between phases when they are switched on and switched off. It was observed that the switching pattern is random, both in duration as well as in the sequence of the phase switching. This arbitrary delay is due to the mechanical tolerance of the circuit breaker. The longest delay time observed during the measurements was 300 µs between the first phase was switched until the third phase was switched. However the delay times observed are less than the typically times of 3 - 5 ms. (25) In order to compare simulation and measurements the delay has been implemented in the PSCAD model. For example for one measurement it was observed that phase b and phase c had a delay of 260 µs respectively 300 µs compared with the switching of phase Chapter 8 PSCAD model validation and analysis 56 a. So in order to include the delay in PSCAD the switching of phase b and phase c have been delayed 260 µs and 300 µs respectively. The conductors where grounded at both ends after each disconnection in order to discharge the cables, so the initial conditions for each switch on measurement where the same. 8.2 Energization of the cable The value the overvoltage depends on the moment at which the connection is done. The worst case of overvoltage occurs when the connection is made when one phase voltage is at its peak value. On the other hand, the lowest transient occurs if all the phases crosses zero at the instant of switching (requires synchronous switching). 8.2.1 Sending end voltage In fig 8-1 a comparison of measurement and simulation results for the sending end voltages during energization are shown for each phase. It can be seen that there exists a good agreement between measurement and simulations. Chapter 8 PSCAD model validation and analysis 57 fig 8-1 Energization - phase a, phase b and phase c sending end voltages - measurement and PSCAD model Chapter 8 PSCAD model validation and analysis 58 In fig 8-2 a zoomed in comparison during the transient can be seen for each phase. fig 8-2 Zoom in of phase a, phase b and phase c sending voltages - measurement and PSCAD model Chapter 8 PSCAD model validation and analysis 65 fig 8-7 Zoom in of phase a, phase b and phase c busbar voltage – measurement and PSCAD model It can be seen that there exist more damping in the simulation. 8.2.5 Current (sending end) In fig 8-8 is shown the measured and simulated currents at the sending end during energization for each phase. Chapter 8 PSCAD model validation and analysis 66 Chapter 8 PSCAD model validation and analysis 67 fig 8-8 Phase a, phase b and phase c sending end current – measurement and PSCAD model It can be seen that after the transient a sinusoidal current in the cables is present although the receiving end is open circuited. This current is due to the charging of the cable capacitors. The highest current measured is 1,355 kA and simulated is 1,187 kA. In fig 8-9 a zoomed in plot of the currents for each phase at the instant of switching is shown. Chapter 8 PSCAD model validation and analysis 68 fig 8-9 Zoom in of phase a, phase b and phase c sending end current – measurement and PSCAD model From fig 8-9 it can be seen that there exist a good agreement between simulation and measurement in the beginning. As the simulation voltage is set equal to the measured voltage the current is dependent of the characteristic admittance Y c (i = Y c · u, where u and i are voltage and current vectors respectively). Y c is affected by inductance, capacitance and resistance. (16) Since the good agreement present in the beginning it is assumed that the model is quite accurate. It can be seen that the damping of the current is low compared to the voltages shown in section 8.2.1 and 8.2.2. Further it can be seen that the simulation results is delayed compared with the measurement. This can be Chapter 8 PSCAD model validation and analysis 69 caused by inaccuracies of Y c or by the propagation mode of the reflected surge (this will be evaluated in 8.4.2). (16) 8.3 De-energization In this section the results obtained for voltage and current when the cable is being deenergized. Only the current and sending end voltage is presented since the receiving end voltage is identical with the sending end (no Ferranti / reflection is present). The busbar voltage is also not presented since there is no transient occurring. 8.3.1 Sending end voltage The measured and simulated sending end voltages are presented in fig 8-10. fig 8-10 Sending end voltages measured and simulated during cable de-energization Chapter 8 PSCAD model validation and analysis 70 From fig 8-10 it can be seen that there is a large difference between the measured and simulated results. From the measurement it can be seen that phase a voltage is close to its peak value at the moment of the switching and it remains constant for a short period of time before it suddenly decreases The value of phase b has a less voltage value than phase c and remains constant for a longer time than phase a. Finally phase b has the lowest value at the moment of switching and remains at this value for a longer time than the other phases. For the simulation it can be seen that the phase voltages are slowly going towards zero (complete discharge after 3 s). In fig 8-13 is shown simulation and measurement of each phase. Chapter 8 PSCAD model validation and analysis 71 fig 8-11 De-energization phase a, phase b and phase c sending end voltages - measurement and PSCAD model From fig 8-11 it can be seen that simulation and measurement are in good agreement before the voltage dips occur. The reason for the dip in the measurement is caused by saturation of the voltage transformer and will be treated in section 8.3.3. 8.3.2 Sending end current The measured and simulated currents are presented in fig 8-12. Chapter 8 PSCAD model validation and analysis 72 fig 8-12 Measured and simulated current during de-energization As can be seen from fig 8-12 there is noise present in the measurement, which is not noticeable for the energization (fig 8-8). However it is also present in fig 8-8 but since the current scale is much higher it is not noticeable. It is assumed that the noise originates from the sampling frequency of the omicron. From fig 8-12 it can be observed that the currents are not interrupted at their respective zero crossing. As explained in section 1.6 capacitive currents can be interrupted at any instant since the magnitude is low. In the following subsection an analysis of the difference between simulation and measurement is made. Chapter 8 PSCAD model validation and analysis 73 8.3.3 Analysis of the measured voltages and current during de-energization The measured voltage during de-energization was presented in fig 8-10 and is given again in fig 8-12 for convenience. fig 8-13 Measured voltage sending end during cable de-energization As can be seen from fig 8-13 the voltage on each phase is kept at a constant value at for a time after the switch off operation. After a time a sudden dip in the voltage followed by what appears to be a 1 st order system decaying. This is due to saturation of the transformer core which causes capacitor discharging to ground through the primary winding of the transformer. From the moment of the disconnection the cable acts like a DC voltage battery and therefore the primary winding works like a short circuit to ground. This current causes winding heating and if the time between each switching is short, the transformer is not cooled down and could be damaged. Further an overheating of the transformer can result in inaccurate measurements. (26) The actual behaviour of the de-energization in fig 8-13 can be explained by the nonlinearity of the voltage transformer, which together with the cable capacitance causes ferroresonance. Ferroresonance is a phenomenon that can occur when the cable is disconnected so that the measuring transformers on the cable side are forming a resonance circuit with the cables capacitances. (27). In fig 8-14 the equivalent circuit after disconnection is shown. In fig 8-15 a general piecewise linear magnetization curve for the voltage transformer (VT) is shown. Chapter 8 PSCAD model validation and analysis 74 fig 8-14 Simplified equivalent diagram of cable deenergization connected to a voltage transformer. The losses are composed by the losses in the cable and in the transformer fig 8-15 Simplified magnetisation curve for transformer coil An explanation of this follows on basis of phase b voltage shown in fig 8-16, where the first instant after de-energization is shown. t1t2t3t4t5t6 L3 L4 L1 L1 L3 L2 fig 8-16 First 270 ms after de-energization of phase B with indication of different values of inductance due to non linear transformer magnetisation curve Chapter 8 PSCAD model validation and analysis 81 fig 8-19 tolerance graphs for the sending end voltage measurement in the three phases. Chapter 8 PSCAD model validation and analysis 82 fig 8-20 Tolerance graphs for the receiving end voltage measurement in the three phases Overall Analysis of the tolerance of the measuring equipment The above analysis of the measuring equipment shows that the overall tolerance does not affect the results significantly. 8.4.2 Other factors that can affect the difference between measurement results and simulations In the above section it was found that the tolerance of the measuring equipment does not affect the results significantly. In this section an investigation and evaluation of other factor that may influence the difference between simulation and measuring result: • How much of the grid is included in the model In the model development described in chapter 5 only a part of ENV A/S grid was implemented in the model. • Non symmetrical cable layout In the model the layout is assumed to be symmetrical for the whole cable length. This is assumed not to be the case for the actual cable. • Inaccuracy of the characteristic admittance Y c in PSCAD Chapter 8 PSCAD model validation and analysis 83 If the geometry is not carefully inserted in PSCAD or wrong information given inaccuracies in the characteristic admittance Y c may occur. This can result in higher damping for the simulation, which was evident from the voltage comparison. Further it can result in a delay which is evident for the current comparison. (16) The inaccuracy can be a result of the non symmetrical cable layout. • Wave mode propagation From the current comparison in fig 8-9 it can be seen that there is good agreement in the beginning before reflected waves return to the sending end. Since the simulation voltage is set equal to the measured one, it can be assumed that the characteristic admittance Y c is right. (16) When the travelling wave reaches the receiving end it will be reflected in different modes since the sheaths are grounded. This means that a fraction of for example the reflected wave of phase a will propagate back to the source through the sheath of phase b (and c) (intersheath mode). The distribution of current in the intersheath mode is dependent of proximity effect, which is not included in PSCAD package. (16) In order to make an assessment of the wave mode propagation, modal analysis should be employed as explained in (16). However this is not done due to the practical implication as well as the limited time available at the substations. • Omicron sampling frequency The sample frequency of the omicron does not allow an accurate investigation of the impact of the travelling wave. The travelling time of the wave was calculated to 66,7 µs in chapter 6, so the wave returns to the sending end 132 µs after the energization. With a sampling frequency of 28 kHz the samples are taken with a time step of 35,7 µs which is high. • Grid impedance The grid impedance is calculated for steady state in chapter 5. Further it is being implemented with lumped parameters. The grid impedance should have been Chapter 8 PSCAD model validation and analysis 84 implemented with distributed and frequency dependent parameters in order to give a more accurate behaviour of the system. • Transfer function of the measuring transformers The behaviour of the measuring transformers with respect to frequency can affect the difference between measurement and simulation since the transformers have not been implemented in PSCAD. The internal resonance of the voltage transformer is: (28) ( ) 1 2· · 1 2· · t ft LC π = − (8.4) Where t is the transformer ratio. It can be seen that the resonance is inversely proportional to the transformer ratio, which means that the resonance frequency is low and can be influencing the transformers accuracy for transient measuring. Further the de-energization comparison shows large deviation between measurement and simulation due to saturation. 8.5 Worst case overvoltages and inrush current analysis On basis of the comparisons done in the above, the PSCAD model is considered valid at this point. As explained in section 1.4 and 1.7 the worst case of overvoltage and inrush current is occurring if one of the phase voltages is at its peak at the moment of switching. The measured switching was not occurring at the peak voltage, so in order to evaluate the worst case the PSCAD model will be used. Simulation results for the sending, receiving end and busbar voltage are shown in Fig 8-21. Chapter 8 PSCAD model validation and analysis 85 Fig 8-21 Simulated sending end, receiving end and busbar voltages The current at the sending end at the moment of the switching is shown in fig 8-22. Chapter 8 PSCAD model validation and analysis 86 fig 8-22 Sending end current– PSCAD model In table 8-3 are summarized the worst case simulated overvoltage and inrush current. The inrush current will be used in section 8.5.1 to evaluate the withstand ability of the circuit breaker. The result in the table will be used as a comparison in chapter 9, where methods in order to minimize inrush current and overvoltages are described and implemented in PSCAD. table 8-3Worst case simulation results Case Peak value simulated [kV] [1 p.u. = (63,2 kV·√2/√3)] ] Peak value simulated [kA] Switch on Sending end 1,11 1,218 Receiving end 1,36 - Before CB 1,11 - 8.5.1 Inrush current and circuit breaker As explained in section 1.7.1 the combination of high peak / high frequency stresses the circuit breaker. It was explained that the rated current and frequency for circuit breakers are I bi,N = 20 kA peak and f bi,N = 4250 Hz. The product of I bi · f bi must not exceed 85·10 6 A/s. From the simulation was obtained the following: I bi = 1,218 kA and f bi = 3,1 kHz which gives I bi,N · f bi,N = 3,78·10 6 A/s which is much less than 85·10 6 A/s. Chapter 8 PSCAD model validation and analysis 87 8.6 Velocity of the travelling wave In fig 8-23 are shown simulation of sending and receiving end. On basis of the simulation the time delay is found to be 66,7 µs. From this the wave velocity is found to be 180000 km/s. This value is used to obtain a value for the inductance in chapter 6 in order to calculate the resonance frequencies. fig 8-23 Sending and receiving end voltages simulated in order to obtain the wave velocity Chapter 8 PSCAD model validation and analysis 88 8.7 Chapter summarization In this chapter a comparison with PSCAD simulation and field measurement of cable switching is made. This is done by comparing simulation/measurement of sending end voltages, receiving end voltages, busbar voltages and inrush currents. The results can be seen from fig 8-1 to fig 8-12. From the comparison it can be seen that measurement and simulation are to a certain degree in good accordance with each other. It is observed from the voltage measurement that the simulations are more damped than the measured ones. The highest measured peak voltages are -56,03 kV and -69,5 kV for sending and receiving end respectively. The higher voltage in the receiving end is what is expected since the energy content of the travelling wave is stored in the electric field, when the wave encounters an open circuit. For the inrush current there also exist a good agreement between measurement and simulation before the reflected wave returns to the sending end. Since the voltage used in the simulation is the same as the measured it is assumed that the developed model is valid since the transfer function from voltage to current (characteristic admittance) depends on the input data in PSCAD such as physical dimensions, permittivity and resistivity of the medias. When the surge is reflected to the source deviations between measurement and simulation occurs. This is assumed to be caused by the fact that the reflected wave propagates in different modes (ground, intersheath etc.). The intersheath mode is dependent on current distribution, which again depends on proximity effect for very high frequencies. The proximity is not included in the PSCAD software. An analysis of the errors caused by the measuring equipment has been made and it has been found, that the tolerances is not affecting the differences between measurement and simulation. The developed PSCAD model is regarded as being validated and will be used in chapter 9 where methods in order to minimize the overvoltages will be investigated. Chapter 9 Minimization of the switching overvoltage 89 9 Minimisation of the switching overvoltage In this chapter methods for minimize the transient overvoltages during the energization of the cable are presented. Two methods are investigated: synchronous switching of the circuit breaker and the use of pre-insertion resistance during the switch on. The methods will be implemented in the PSCAD model and their effect on the overvoltage and inrush current will be evaluated. 9.1 Background for overvoltage minimisation The overvoltages occurring during cable energization can stress the insulation of the system equipment and thereby lower the equipment lifetime. The overvoltages can also propagate to lower voltage levels, where they may cause a breakdown of electronic equipment. (29) Another problem which has, according to Magnus L. Hansen, been of concern for ENV A/S during the latest purchase of circuit breakers in 2009, that the high frequency inrush current is close to the withstand limit of the circuit breakers. As explained in section 1.7 connecting a cable to a busbar with already energized cables connected is electrically equivalent to capacitor bank energization. Therefore some of the existing methods for capacitor banks can be utilized in limitation of inrush current and transient voltage during cable energization In this chapter two methods to minimize the switching currents and voltages are described and implemented in PSCAD. The methods are: • Pre-insertion resistor in the circuit breaker • Synchronous closing of the circuit breaker Chapter 9 Minimization of the switching overvoltage 90 9.2 Pre-insertion resistor Circuit breakers can be equipped with an internal pre-insertion resistor as shown in fig 9-1. fig 9-1Schematic of pre-insertion resistor in the circuit breaker. Switch S 1 is switched on first and S 2 is switched on 10 ms after fig 9-2 Equivalent diagram with a cable matching pre-insertion resistance is connected during energization If a resistor is connected in series with the cable, the travelling wave (hence the switching current and voltage) will be reduced. This is done by dividing the switching action into a multistep operation, by first switching on the pre-insertion resistor R p by switch S 1 . The insertion time is typically 8 - 12 ms before R p is shortened by switching S 2 . (30) During the operation of S 2 a new switching transient occurs. During energization of a cable the receiving end is open circuited as indicated in fig 9-2. For this case when the value of the resistor is equal to the characteristic impedance of the cable so, according to voltage division, only half of the source voltage is at the sending end of the cable. This way the voltage is 0,5 p.u. in the sending end of the cable and 1 p.u. in the receiving end. This doubling of the voltage can be explained on basis of energy conservation: Under lossless conditions the energy of the travelling wave is equally distributed between the electric and magnetic field. (10) So when the current wave encounters the open end of the cable it goes to zero and the voltage doubles since the energy stored in the magnetic field is converted into the electric field. However for practical condition as shown in section 8.2.3 the receiving end is only 1,24 times the sending end due to damping (resistance). Chapter 9 Minimization of the switching overvoltage 97 9.4 Chapter summarization In this chapter two methods in order to minimize overvoltage and inrush current during cable energization has been described and implemented in PSCAD. The methods are: • Pre-insertion resistor in the circuit breaker • Synchronous closing of the circuit breaker On basis of simulation it has been shown that the two methods effectively minimize the switching transient. The synchronous closing is ideally removing the overvoltage inrush current. For practical purpose however the switching will not occur exactly when the phase voltage is crossing zero due to mechanical tolerances. The basic insulation level (BIL) for 72,5 kV systems is 140 kV. (29) The observed overvoltages are well within this limit, however as described in the beginning of this chapter the overvoltages stresses the equipment and may propagate to lower voltage levels, which may justify the use of overvoltage minimization methods as described in this chapter. Chapter 10 Conclusion 10 Conclusion This report deals with the overvoltages during energization of a cable located in a 60 kV cable network. An analysis of the resonance frequencies that are causing the overvoltages are investigated and calculated for a specific cable located in ENV A/S 60 kV cable network. An investigation of the capacitive inrush current from already energized cables has also been made, the so-called back to back switching. In order to do an assessment of the switching overvoltages and inrush current a part of ENV A/S network has been implemented in the transient software PSCAD. In order to verify the simulation field measurements has been made of switching in and out of the specific cable. The resonance frequencies causing the overvoltages have been analysed and calculated by using three approaches namely: Analytic approach using standing wave theory, by using the equivalent π model where skin effect have been included and finally by doing a frequency scan in the PSCAD model. There is a good agreement between the results of the three methods. However the inductance used in analytic approach as well as in the equivalent π model has been obtained using the travelling time which has been found in PSCAD. This indicates a dependency between the methods. In order to eliminate the dependency, the travelling time of the propagating wave could have been measured. However, since this requires a large amount of preparation and the time available during the measurement at the substations where limited, this has not been done. A comparison between measurement and simulation shows good agreement before reflections from the receiving end emerges at the sending end. This indicates that the PSCAD model is properly designed since the simulated voltage is set equal to the measured one. It is assumed that the deviation is caused by the fact that the reflected wave propagates in different modes (ground, intersheath etc.). The intersheath mode is Chapter 10 Conclusion 99 dependent on current distribution, which again depends on proximity effect. The proximity effect is not included in the PSCAD software. An assessment of the deviation has been made, including an analysis of the tolerance of measuring equipments influence on the result. It was found that the tolerances does not affecting the differences between measurement and simulation. It can be concluded that the PSCAD model gives a rather good prediction of the switching overvoltages as well as inrush currents. An analysis of the circuit breaker withstand ability has been made and compared with the limits in IEC 62271-100 1 st edition. It was found that the frequency and current during energization is well within the limit. However, the relatively high current/frequency stresses the circuit breaker. Measurement of the voltages during de-energization shows that the voltage transformer goes into saturation and the cable is discharges across the primary of the transformer. The voltage transformer has not been implemented in PSCAD, since the data needed was not accessible, such as the saturation curve etc. Instead an in-depth analysis of the non-linear saturation causing the discharging has been made. This approach is concluded to be sufficient since the aim of the project is to investigate the overvoltage during energization as well as inrush current. In order to minimize the overvoltages two methods are investigated and implemented in the PSCAD model. The strategies are pre-insertion resistor and synchronous closing of the circuit breaker. Both methods show good capability of limiting both the overvoltages as well as the inrush currents. Chapter 10 Conclusion 100 10.1 Future work Below are shown a list of subjects that could be investigated / implemented in a future work: • Measurement of the travelling time of the switching surge using a GPS transmitter The measured travelling time can be used as a part of the PSCAD model validation • Implement the measuring transformers in PSCAD in order to investigate the saturation of the transformers and to investigate if the non-measuring of the current during de-energization is caused by saturation • Field measuring of the resonance frequencies using an AC generator with variable frequency. The measured resonance frequencies can be used as a part of the PSCAD model validation Chapter 11 Literature 101 11 Literature 1. Gudmundsson, Gnyr. Power System Calculations. 2. Wittrup, Sanne. http://ing.dk/artikel/96980-danmark-samler-topkompetencer-paa-lange- kabler. [Online] 13 03 2009 . 3. Xu, Zhihan. Power Cable Protection in Transmission System. 4. Vørts, S. Elektriske Fordelingsanlæg 4.th. 1990. ISBN-13 978-87-502-0707-8. 5. Energinet A/S. Comprehensive use of High Voltage AC cables. 2006. 6. Energinet.dk A/S. Infoblade om eltransmissionssystemet. 2007. 7. da Silva, F. Faria, Bak, C.L and Hansen, M.L. Back to back energization of a 60kV cable network - inrush currents phenomenon. 8. van der Sluis, Lou. Transient in Power Systems. s.l. : John Wiley & Sons Ltd, 2001. ISBN - 0-471-48639-6. 9. Alexander, C.K and Sadiku, M.N.O. Fundamentals of Electric Circuits, 3rd Edition. s.l. : McGraw-Hill, 2000. ISBN-13: 9780072493504. 10. Greenwood, Allan. Electrical Transienst in Power Systems 2nd. ed. s.l. : John Wiley & Sons, Inc., 1991. ISBN-0-471-62058-0. 11. Holbøll, Joachim. High Voltage Cables, An Introduction. 2007. 12. Thue, William A. Electrical Power Cable Engineering. 1999. ISBN-0824743032. 13. Brugg Cables. High voltage XLPE cable systems, Technical user guide. 14. Bak, C.L and Hansen, M.L. ENV Trancient Analysis of the ENV Net A/S Network - TheSBAnet. s.l. : ENV A/S, 2009. 15. The Manitoba HVDC Research. EMTDC User Guide V4.2. s.l. : The Manitoba HVDC Research, 2005. 16. Gudmoundsdottir, Unnur Stella and al., et. Field Test and Simulation of a 400 kV Crossbonded Cable System. NOT PUBLISHED. 17. Keri and Gole. "Modelling and Analysis of System Transients Using Digital Programs (draft)". 1998, IEEE Special Publication,1998. Chapter 11 Literature 102 18. Ibrahim, A. I. and Dommel, H. W. "A Knowledge Base for Switching Surge Transients". 2005, Presented at the International Conference on Power Systems Transients (IPST’05) in Montreal, Canada on June 19-23, 2005. 19. Fishbane, Gasiorowicz and Thornton. Physics for Scientists and Engineers with Modern Physics 3th. ed. s.l. : Person, 2005. ISBN-13-191182-1. 20. Cheng, David K. Field and Wave Electromagnetics, 2nd. Ed. s.l. : Addison Wesley Publishing Company, 1983. ISBN-0-201-01239-1. 21. Kuphaldt, Tony R. Lessons In Electric Circuits, Volume II – AC. 2007. 22. Sadaat, Hadi. Power System Analysis. s.l. : McGraw-Hill, 1999. ISBN-0-07-012235-0. 23. Arrilaga, J. and Watson, N.R. Power System Harmonics 2nd ed. 2003. ISBN- 9780471927600. 24. Tleis., Dr Abdul Nasser Dib. Power Systems Modelling and Faults Analysis. s.l. : Elsevier Ltd., 2008. ISBN-13: 978-0-7506-8074-5. 25. Ryan, H. M. High Voltage Engineering and Testing. s.l. : Peter Peregrinus ltd., 1994. ISBN-0-86341-293-9. 26. ABB. Outdoor Instrument Transformers Application Guide 2nd. ed. 2005. 27. Groupe Schneider. Cahier technique n° 190 Ferroresonance. 28. Meliopoulos, et al. Transimission Level Instrument Transformers and Transient Event Recorders Characterization For Harmonic Measurements. 1993. 29. Kuffel, E. High Voltage Engineering - Fundamentals 2nd ed. s.l. : Newnes, 2000. ISBN- 978-0750636346. 30. da Silva, F. Faria, et al. "Use of a Pre-Insertion Resistor to Minimize Zero-Missing Phenomenon and Switching Overvoltages". 2009, Power & Energy Society General Meeting, 2009. PES '09. IEEE. 31. Begamudre, Rakosh Das. Extra High Voltage AC Transmission Engineering 3rd Ed. s.l. : New Age International Ltd, 2006. ISBN-8122417922. 32. EC&M. http://ecmweb.com/mag/electric_trouble_capacitors_part_2/. [Online] [Cited: 07 05 2010.] 33. Guðmundsdóttir, Unnur Stella. "Modelling of High Voltage AC cables". 2009, Paper submitted to the International Conference on Power System Transients(IPST2009)in Kioto,Japan June 3-6-2009. Chapter 11 Literature 103 34. Gustavsen, B., Martinez, J. A. and Durbak, D. "Parameter Determination for Modeling System Transients — Part II: Insulated Cables". 2005, IEEE Transactions on Power Delivery, Vol. 20, No. 3, July 2005. Appendix A Cable parameter calculations A Appendix cable parameter calculations In order to electrically describe a cable, the following parameters will be included: • Series impedance (resistance and inductance) • Shunt admittance (capacitance. The conductance is assumed very small and is neglected in this report) 1) Series impedance The series impedance is composed of a resistor and an inductance. For calculation of these parameters, it is required to have knowledge of the conductor material, the physical dimensions, construction and soil resistivity. AC resistance The cable consists of many layers. In general, there are three metallic layers (core, sheath, armour. The cable under investigation in this report does not have an amour, which is normally used for marine cables). Each of the layers has an AC resistance, which can be calculated as. . 1 .( ) AC DC s p R R y k k   = + +   [ ] / km Ω ( 1) A − where k s is skin effect factor, k p proximity effect factor and y is a constant (y = 1 for single-core, two-core and three-core cables and y=1.5 for pipe-type cables). (24) DC resistance is given by 20 . .[1 .( 20)] DC l R A ρ α ϑ = + − [ ] / km Ω ( 2) A − where ρ is resistivity of conductor (Ωm), l is length of cable (1km), A is cross-section of conductor (mm 2 ), α 20 is percentage change in resistivity per unit temperature (°C -1 ) and ϑ is temperature of conductor (°C). The cable under investigation (PEX-M-AL-LT 72kV - 400mm 2 ) has a core made of aluminium. DC resistance of the core per 1 km is. Appendix A Cable parameter calculations 105 8 2 2 2 1000 2,82 10 0,07914 0,01065 DC Al c l m R m km r m ρπ π − Ω = ⋅ = ⋅ Ω ⋅ = ⋅ ⋅ ( 3) A − where r c is radius of core. Due to skin effect the resistance is dependent on the frequency according to formula below. 4 4 2 0 2.8 0,8 192 0,0563 0,0177 0,136 for 2.8 3.8 0,354 0,733 3,8 z z z ks z z z z z  < ≤ ⋅ +   = ⋅ − ⋅ − < ≤  ⋅ − >    ( 4) A − where z is frequency dependent and for solid or normally stranded conductor is: 4 8 10 DC f zR π =⋅ ( 5) A − Proximity effect factor is in this report neglected as well as resistance of the sheath.(24) For frequency of 50 Hz the skin effect factor is close to zero and thus the value of AC resistance is the same as DC resistance. Inductance The inductance of a cable system depends on the cable layout and on the external conductor diameter. In fig A-1 and A-2 are the two basic types of cable layouts presented. fig A-1 Trefoil layout fig A-2 Flat layout Appendix A Cable parameter calculations 106 The cable under investigation has a trefoil layout. The inductance for this layout can be calculated as: (4) 4 4 2 28,15 2 10 ln 2 10 ln 188,63 / 0,7788 0,7788 28,15 a mm L H km r mm µ − − ⋅     = ⋅ = ⋅ =     ⋅ ⋅     ( 6) A − where a is distance between phases and r is outer radius of the core conductor. 2) Shunt capacitance The capacitance of the cable depends on the type of insulation (its relative permittivity) and the diameter of the conductor and insulation. There exist two capacitances. The first is between the core and sheath and second between the sheath and earth. Since each cable has its own screen there is no capacitance between the phase conductors. (24) fig A-3 Cable cross-section a) Capacitance between the core and sheath , , 0,0556 ln i CS i out i in Cr r ε ⋅ =         [ ] / / F km phase µ ( 7) A − where ε i is the relative permittivity of main insulation (ε XLPE = 2,3), r i,in and r i,out are the inner and outer radii of the main insulation, respectively.