Aalborg Universitet. Published in: I E E E Transactions on Power Delivery. DOI (link to publication from Publisher): /TPWRD.2010.

Transcription

1 Aalborg Univeritet Method to Minimize Zero-Miing Phenomenon Silva, Filipe Miguel Faria da; Bak, Clau Leth; Gudmunddottir, Unnur Stella; Wiechowki, W.; Knardrupgård, M.. Publihed in: I E E E Tranaction on Power Delivery DOI (link to publication from Publiher):./TPWD.. Publication date: Document Verion Accepted author manucript, peer reviewed verion Link to publication from Aalborg Univerity Citation for publihed verion (APA): da Silva, F. M. F., Bak, C. L., Gudmunddottir, U. S., Wiechowki, W., & Knardrupgård, M.. (). Method to Minimize Zero-Miing Phenomenon. I E E E Tranaction on Power Delivery, (), -. DOI:./TPWD.. General right Copyright and moral right for the publication made acceible in the public portal are retained by the author and/or other copyright owner and it i a condition of acceing publication that uer recognie and abide by the legal requirement aociated with thee right.? Uer may download and print one copy of any publication from the public portal for the purpoe of private tudy or reearch.? You may not further ditribute the material or ue it for any profit-making activity or commercial gain? You may freely ditribute the UL identifying the publication in the public portal? Take down policy If you believe that thi document breache copyright pleae contact u at vbn@aub.aau.dk providing detail, and we will remove acce to the work immediately and invetigate your claim. Downloaded from vbn.aau.dk on: december,

2 Page of IEEE PES Tranaction on Power Delivery TPWD-- Abtract With the increaing ue of high-voltage AC cable at tranmiion level, phenomena uch a current zero-miing tart to appear more often in tranmiion ytem. Zero-miing phenomenon can occur when energizing cable line with hunt reactor. Thi may coniderably delay the opening of the circuit breaker, leaving the ytem unprotected and vulnerable to failure. Method to prevent zero-miing phenomenon are till being tudied and compared in order to identify effective countermeaure. Thi paper contribute to thee effort, by preenting everal countermeaure that can be applied to reduce the hazard of zero-miing phenomenon. The author dicovered that thi phenomenon can be eliminated, merely by uing an extra circuit breaker or a preinertion reitor. Index Term Power Cable, AC Circuit Breaker, Shunt eactor, Switching Tranient, Level-croing problem Z Method to Minimize Zero-Miing Phenomenon F. Faria da Silva, C. L. Bak, U. S. Gudmunddottir, W. Wiechowki and M.. Knardrupgård I. INTODUCTION EO-MISSING phenomenon i defined a an AC current not croing zero value during everal cycle. If a current doe not cro zero value it i not poible to open the circuit breaker without rik of damage, except if the circuit breaker i deigned to interrupt DC current or open at a non-zero current value [][]. Becaue of the large capacitive reactive power of HVAC cable, hunt reactor are needed for power compenation. For unloaded cable ytem, the hunt reactor current i almot in phae oppoition to the current in the cable, reducing the amplitude of the reultant AC component through the circuit breaker. A the current in the hunt reactor ha a tranient DC component, the reulting current in the circuit breaker may have a DC component larger than it AC component. When Manucript received September,. Thi work wa upported in part by the Danih Tranmiion Sytem Operator, Energinet.dk. F. F. da Silva i a PhD tudent at the Intitute of Energy Technology, Aalborg Univerity, Aalborg, Denmark ( ff@iet.aau.dk). C. L. Bak i with the Intitute of Energy Technology, Aalborg Univerity, Aalborg, Denmark ( clb@iet.aau.dk). U. S. Gudmunddottir i a PhD tudent at the Intitute of Energy Technology, Aalborg Univerity, Aalborg, Denmark ( ug@iet.aau.dk). W. Wiechowki i a Senior Sytem Analyt at the Planning Department of Energinet.dk ( wwi@energinet.dk) M.. Knardrupgård i with the Planning Department of Energinet.dk ( mra@energinet.dk). thi happen, the current paing through the circuit breaker doe not cro zero until the DC component become maller than the AC component. During it energization the cable i unloaded, and the reitance of the ytem (cable+hunt reactor()) i very mall. A a reult, the DC component may take everal econd to be damped, period during which the circuit breaker cannot be opened. Thi paper i an extenion of [], and for a Hz power frequency it decribe zero-miing phenomenon and preent countermeaure that can be ued to avoid it. The countermeaure are divided into two type: Cae where the hunt reactor i directly connected to the cable and cae where the hunt reactor i connected to the cable via a circuit breaker. II. ZEO-MISSING PHENOMENON AND SWITCHING OVEVOLTAGES A. Baic Circuit: Inductor in Parallel with a Capacitor An eay way of undertand zero-miing phenomenon i by analying an inductor in parallel with a capacitor of equal impedance. In thi ituation the current in the capacitor and inductor have equal amplitude and are in phae oppoition. The current in the inductor can alo have a DC component, whoe value depend on the voltage at moment of connection. If the inductor i connected at peak voltage the current at t( + ) i zero, if it i connected for zero voltage the current ha a peak value at t( + ). A the current in the inductor mut maintain it continuity, and it wa zero at t( - ), if the voltage i not at a peak value during connection, a DC component will appear in the inductor current to maintain it continuity. The DC component i equal to minu the value of the AC component at t( - ) []. If there i no reitance in the ytem, the DC component i not damped and it will be maintained infinitely. In reality there i alway ome reitance and the DC component diappear after ome time. Fig. how an inductor in erie with a reitor, both of them in parallel with a capacitor. The reitance i time maller than the inductor reactance, which i equal to the capacitor reactance. Fig. how a imulation of Fig.. The circuit breaker cloe when the voltage i croing zero, and therefore the DC component in the inductor i maximum. The inductive and capacitive AC component cancel out (IL and IC

3 IEEE PES Tranaction on Power Delivery Page of TPWD-- have equal amplitude and are in phae oppoition) and the current I contain only the decaying DC component Fig. Equivalent cheme of an inductor in erie with a reitor, both in parallel with a capacitor Time [] Fig. Current in the inductor (IL, dahed line), in the capacitor (IC, dotted line) and the um (I=IL+IC, olid line) The behaviour of a ytem coniting of a hunt reactor and a cable i not very different from the one depicted in Fig.. The hunt reactor can be modelled a an inductor in erie with a reitor, and the cable i mainly a capacitive hunt element []. There are, however difference between the behaviour of a imple LC circuit and a phyical cable/hunt reactor ytem, a for intance witching overvoltage. Switching overvoltage occur due to the charging of the cable' capacitance and energy ocillation between the cable' capacitance and inductance []. A for zero-miing phenomenon, the value of witching overvoltage depend on the voltage value when connecting the cable/reactor ytem. However, to avoid zero-miing phenomenon the connection hould be made when the voltage i at it peak, wherea the oppoite applie when it come to avoiding witching overvoltage [][]. According to [], when the hunt reactor i directly connected to the cable it i neceary to chooe between avoiding either zero-miing phenomenon or witching overvoltage. Thi paper will how that it i poible to avoid both by applying pecific countermeaure. B. Sytem uing Cable' Pi-model For analyi purpoe the hunt reactor had been modeled a an inductor in erie with a reitor and the cable i repreented by it equivalent pi-model (ee Fig. ). Fig. Equivalent cheme of a hunt reactor and a cable: V -Voltage Source; S-Shunt reactor reitor; L S-Shunt reactor inductor; -Cable' erie reitor; L-Cable' erie inductor; C-Cable' hunt capacitor The ytem of Fig. i decribed by (). The circuit breaker current I, equal to I S +I C +I, i obtained from () and hown in (). di V co( ωt) = L + I dt V co( ωt) = Icdt C () di V co ( ωt) = I + L + Idt dt C V ωl t ( ) co arctan I t = ωt I L + A e + + ( ωl ) L V ω co ωt arctan ωc ωl ωc t L π + I e co ω t + V co ωt + ωc aux L Where I A i the initial value of the DC component and i calculated by (). I aux i related with the energization of the inductor and capacitor and i calculated by (). Both depend on the moment when the hunt reactor i connected. I I A V ωl = co ωt arctan + ( ωl ) aux () () L V ω co arctan ωc = () + ωl ωc The equation can be confirmed uing EMTDC/PSCAD to imulate the ytem. Fig. how the current in the circuit breaker uing both EMTDC/PSCAD and () for a ingle phae cable, and a kv voltage ource. The parameter ued in the imulation are baed on a kv, km cable from SAGEM []: C=. µf; L=. mh; =. Ω; for the hunt reactor the parameter are: L S =. H; S =. Ω. Fig. Current I during. for % reactive power compenation In order to have more accurate reult for the imulation intead of uing a pi-model the cable will be imulated by a PSCAD-EMTDC frequency dependent phae model, a it i

4 Page of IEEE PES Tranaction on Power Delivery TPWD-- currently the mot precie method to imulate cable []. The electrical cable parameter are equal to the one previou mentioned for the pi-model. A expected there are mall difference between the two imulation, mainly in the moment following the connection of the cable/hunt reactor. C. Circuit Breaker Two different circuit breaker type can be ued. A firt type that cloe all the phae at the ame time, and a econd type called ingle-pole mode, which cloe the three phae at different moment []. A circuit breaker operating in ingle-pole mode i imilar to three different ingle-phae circuit breaker operating independently. In Fig. an example i hown of the cloing of a circuit breaker operating in thi mode, phae cloe at m, phae T at. m and phae S. m after phae. Fig. Example of a ingle-pole mode operation [] The type of circuit breaker ued ha an influence on the energizing tranient. Fig. and Fig. how the difference between the two mode. In Fig. all the phae cloe when the voltage i zero in the repective phae, therefore the DC component i maximum and the witching tranient minimum in all the phae. In Fig. all the three phae are cloed at the ame time, with phae having a maximum DC component and the other phae having a lower DC component but alo larger witching overvoltage. Voltage [kv] Time [] Time [] Fig. Current I and voltage at the ending end of the cable in a three-phae ytem for a circuit breaker operating in ingle-pole mode (phae : dotted line; phae S: olid line; phae T: dahed line) Voltage [kv] Time [] Time [] Fig. Current I and voltage at the ending end of the cable in a three-phae ytem for a circuit breaker cloing the three phae at the ame time (phae : dotted line; phae S: olid line; phae T: dahed line) III. COUNTEMEASUES WHEN THE SHUNT EACTO IS CONNECTED VIA A CICUIT BEAKE Depending on the ytem load, it may be neceary to connect and diconnect hunt reactor []. In uch ituation the hunt reactor will be connected to the cable via a circuit breaker intead of being directly connected. In thi ituation it i poible to eliminate/reduce the initial DC component imply by controlling the circuit breaker cloing. A. Shunt eactor Connection for a Voltage Peak A explained before, the DC component i zero for a hunt reactor energized at voltage peak. For direct connected hunt reactor, the cable and hunt reactor are energized imultaneouly, and it i not poible to ue thi method becaue of witching overvoltage. But if the hunt reactor are connected via circuit breaker, it i poible to connect the cable when the voltage i zero, and after a hort period connect the hunt reactor when the voltage i at a peak value. For thi countermeaure to be completely effective, the circuit breaker aociated to the hunt reactor mut operate in ingle-pole mode, or it would not be poible to connect all the phae at peak voltage. B. Diconnecting the Shunt eactor before the Cable Zero-miing phenomenon only become problematic if it i neceary to diconnect the cable hortly after it energization. So intead of eliminating zero-miing phenomenon, a poible countermeaure could be to find a method of opening the circuit breaker when deired. Even for a maximum DC component, the current on the hunt reactor (I S ) alway ha a zero croing. It i therefore alway poible to diconnect the hunt reactor from the cable. When the hunt reactor i diconnected both the DC component and inductive AC component diappear. A the cable' circuit breaker current now only ha an AC component the circuit breaker can be diconnect when deired. One advantage of thi countermeaure i that it doe not

5 IEEE PES Tranaction on Power Delivery Page of TPWD-- require a circuit breaker operating in ingle-pole mode. Fig. how an example of countermeaure effectivene. The hunt reactor circuit breaker open at. and the cable circuit breaker at.. A a circuit breaker can only open when the current i croing zero, a delay i required between the two opening order. But a can be oberved, after the diconnection of the hunt reactor there i only AC current without DC offet, and therefore the cable can be diconnected without any rik for the circuit breaker Time [] Fig. Current I when the hunt reactor i diconnected before the cable C. Ue of Several Shunt eactor If more than one hunt reactor i ued to compenate for the reactive power, it i poible to ynchronize their energization thu reducing the rik of zero-miing phenomenon occurring. For zero-miing phenomenon to occur, a hunt reactor ha to compenate more than % of the reactive power generated by the cable. When a cable i compenated by everal hunt reactor, all with the ame compenation level, it i neceary to have more than one connected to have zero-miing phenomenon (unle if it i neceary to compenate more than % of the generated reactive power). Thi countermeaure i demontrated for a ytem with two hunt reactor, each compenating half of the reactive power. The reaoning i imilar for ytem with more hunt reactor. Thi countermeaure involve connecting the econd hunt reactor after the DC component caued by the firt one ha been completely damped. When a hunt reactor compenate % of a cable' reactive power, the amplitude of it AC component i half of the amplitude of the cable' AC component. A thee two current are in phae oppoition, the reulting current I ha an AC component whoe amplitude i equal to that of the hunt reactor' current. The initial DC component i never larger than the amplitude of the hunt reactor AC component, and in the wort cae cenario the minimum peak value of the current I i therefore zero. Fig. give an example of the current in the hunt reactor, cable and circuit breaker, for a ituation where the initial DC component i maximum. After the DC component caued by the firt hunt reactor i damped, the econd hunt reactor i connected. Becaue there already i one hunt reactor connected, the amplitude of I prior to the connection of the econd hunt reactor i half that of the cable' current and equal to the current in the hunt reactor (ee Fig. ). Therefore, when the econd hunt reactor i connected it AC current cancel out the AC current of the ytem, and only the DC component of the econd hunt reactor remain. Thi DC component value i half of what it would have been if only one hunt reactor had been ued, wherea the AC component continue to have the ame amplitude, and a uch the current croe zero ooner. - - Time [m] Fig. Current for a maximum DC component for a hunt reactor compenation half of the cable' reactive power: Solid line: Current in the cable; Dotted line: Current in hunt reactor; Dahed line: Current in the circuit breaker (I ) Fig. and Fig. how the current I before and after the connection of the firt and the econd hunt reactor. Note that a expected the DC current in Fig. i only half of the indicated in Fig., a wa expected Time [] Fig. Current I in the circuit breaker after the connection of the firt hunt reactor (phae : dotted line; phae S: olid line; phae T: dahed line) Time [] Fig. Current I in the circuit breaker after the connection of the econd hunt reactor (phae : dotted line; phae S: olid line; phae T: dahed line) Thi countermeaure doe not eliminate zero-miing phenomenon, it merely reduce it duration. It i therefore till not poible to open the cable circuit breaker in the moment following the energizing of the econd circuit breaker. On the other hand when a cable i energized, problem are more likely to occur immediately after the connection of the cable. A thi countermeaure reult in no zero-miing phenomenon until the econd hunt reactor i connected, the rik to the ytem are reduced. IV. COUNTEMEASUES FO A SHUNT EACTO DIECTLY CONNECTED TO THE CABLE The drawback of the countermeaure preented in the previou ection i that the hunt reactor mut be connected to

6 Page of IEEE PES Tranaction on Power Delivery TPWD-- the cable via a circuit breaker. A a circuit breaker i an expenive piece of witchgear, it will only be intalled if it i abolutely neceary. A common deign choice i to connect the hunt reactor direct to the cable and energize both cable and hunt reactor at the ame time. Thi ection preent two countermeaure that can be ued to avoid zero-miing phenomenon when the hunt reactor i directly connected to the cable. A. Pre-inertion eitor A pre-inertion reitor conit of reitor block connected in parallel with the circuit breaker breaking chamber, and cloe the circuit - m before the arcing contact [] (in thi article the time conidered i m). A pre-inertion reitor can damp the entire DC component in m, thu eliminating zero-miing phenomenon. But for thi happen the pre-inertion reitor value ha to be precie. The incluion of thi reitor change the ytem layout, ee Fig. and compare with Fig.. Jut thi little change i ufficient to change the ytem behaviour o that it i no longer decribed by (), but by (). Fig. Equivalent cheme of the hunt reactor and the cable when uing a pre-inertion reitor ( P) Unlike the differential equation in (), () i not analytically olvable in the time domain []. It i therefore neceary to do a Laplace tranformation in order to olve it. di V = L + I dt V = Icdt C () di V = I + L + Idt dt C I = I + I + Ic V = V co( ωt) p I It i though poible to introduce ome implification in order to obtain a firt approximation of the pre-inertion reitor value. Thi i done by calculating the energy that the pre-inertion reitor hould diipate (). DC W = L ( ) I () The energy diipated in the pre-inertion reitor i calculated by the integral in (), whoe limit are the time during which the pre-inertion reitor i connected.. p () W = Pdt I dt The objective i to calculate p, where both I and I S DC depend on the connection moment and are unknown. For % reactive power compenation, the AC component of the hunt reactor and cable' current cancel each other out, and at the moment of connection the current I i equal to I S DC, wherea both hould ideally be zero after m. Conidering that the current I decreae linearly (thi i an approximation, but a p i large the error i mall), and neglecting S (which i much maller than p ), () can be implified to (), and the value of p i calculated by (). ( ) ( ) I W =. p I. ( ). DC p = L I p = L () L p = (). Becaue of the implification thi method i not alway accurate. If the DC component i maximum the error can be diregarded, but if the DC component i maller, the error increae. The ue of differential equation allow a more accurate calculation of the pre-inertion reitor value, but an iterative proce i required to calculate the value of p. Part of the equation olution i preented in appendix. To perform the iterative proce, a mall program wa written in Matlab. The program increae p, until it reache a value at which the DC component i damped in m. To verify that the DC component i damped, the peak value of I S i calculated m after connection. For that value be equal to the amplitude of the AC component, the DC component mut be equal to zero. So when the calculated value i equal to () plu a mall tolerance the iterative proce top. I peak = + V ( ωl ) () () Fig. - Flowchart of the iterative proce for the calculation of the preinertion reitor value

7 IEEE PES Tranaction on Power Delivery Page of TPWD-- The value of the pre-inertion reitor depend on the initial value of the DC component. A thi value depend on the connection moment, it wa decided to olve the equation for the wort cae cenario, maximum DC component. For that cae the calculated value of p i ideal, wherea for the other cae the error i mall. Solving the differential equation, uing the ytem decribed before, it i obtained Ω a ideal value for the pre-inertion reitor. Fig. and Fig. how two imulation of a circuit breaker equipped with a pre-inertion reitor. In Fig. the circuit breaker operate in ingle-pole mode and cloe each phae for the maximum DC component in the phae. In Fig. the circuit breaker cloe the three phae at the ame time for maximum DC component in jut one of the phae. In Fig. all the three phae are zero during connection. In thi ituation the pre-inertion reitor completely damp the DC component in m and there i no zero-miing phenomenon. A the connection in all the phae i made for zero voltage, the witching overvoltage in the three phae i minimum. For the ituation depicted in Fig. it i not poible to have zero voltage in the three phae when the circuit breaker cloe, and therefore it i neither poible to eliminate the DC component nor completely minimize the witching overvoltage. In one of the phae though there i neither a DC component nor witching overvoltage; thi phae i the one where the voltage i zero at the connection moment. When comparing Fig. with Fig., it can be een how the DC component in the other two phae i maller when the preinertion reitor i ued ( A intead of A) and that there i no witching overvoltage (maximum pu or kv intead of. pu or kv). Voltage [kv] Time [] Time [] Fig. Simulation of cable energizing, for a circuit breaker operating in ingle-pole mode and uing pre-inertion reitor (phae : dotted line; phae S: olid line; phae T: dahed line) Even if the value of the reitor i not ideal, the DC component of the hunt reactor current i alway reduced, and it will be lower than a given maximum. Fig. how the value of the DC component after m for different reitor value when the cable and the hunt reactor are connected for zero voltage. Voltage [kv] Time [] Title [] Fig. Current in the circuit breaker and voltage on the ending end of the cable for a ituation of maximum witching overvoltage, uing a pre-inertion reitor (phae : dotted line; phae S: olid line; phae T: dahed line) The curve in Fig. i non-linear, and for pre-inertion reitor value cloe to the ideal, the DC component i very mall, but for larger difference there i till zero-miing phenomenon during long period of time. If, for intance the value of the pre-inertion reitor value wa calculated uing the energy equation () intead of the differential equation, the initial DC current would be about A, which i time lower than the value of the initial DC component when no pre-inertion reitor i ued ( A). It can therefore be concluded that the method applied in the energy equation can be ued to obtain a firt approximation of the final reitor value. DC component after m [A] Pre-inertion reitor [Ohm] Fig. Initial value of the DC component after bypaing the pre-inertion reitor for different p value, for a phae cloing when the voltage i zero B. Cable Energized from Both End In the previou countermeaure it wa conidered that the cable i energized only at one end while the other end wa open. It i alo poible to energize the cable from both end imultaneouly. When the cable i energized from one end only, there i a pu voltage drop between the cable and the ground, and almot all the voltage drop are due to the cable capacitance to the ground (ee Fig. ). When the cable i energized from both end, the cable reitance and inductance become more relevant, and part of the reactive power i compenated by the grid intead of being

8 Page of IEEE PES Tranaction on Power Delivery TPWD-- olely compenated by the hunt reactor. Therefore the current in the cable i no longer fully cancelled out by the hunt reactor current, and there i an AC component in the current going through the circuit breaker. Fig. how a implified model for a cable being energized from both end. By Ohm' law the current I C only depend on V, wherea the current I depend more on the cable reitance and inductance. If, however the cable wa energized from one end only, it would be the cable capacitance to define mot of the current I value. The current I ha the ame DC component a before, but now it alo ha an AC component, reducing the minimum value of I. The current in the econd generator (I f ) ha an AC amplitude that i almot equal to the one of I but without the DC component (the hunt reactor i in the other cable' end). Therefore it i poible to open the circuit breaker connected to the econd generator at any time. In real cable the capacitance i pread along the cable, and it i not poible to do a o implitic analyi, but the reaoning i imilar. Fig. Model for a cable energized from both end Fig. how the current I for a voltage that i the ame at both terminal terminal. I i hown both for cable energization from one end and both end, repectively. It can be oberved that the DC component i equal in both ituation, but for the cable energied from both end there i alo an AC component whoe amplitude i about half that of the cable' AC current Phae (One End) Phae S (One End) Phae T (One End) Phae (Two End) Phae S (Two End) Phae T (Two End) Time [] Fig. Current in the circuit breaker when the cable i energized from both end and the voltage i equal in both terminal (ocillating line) or jut from one end (flat line) Zero-miing phenomenon doe not diappear by energizing the cable from both end. But, if the voltage i not the ame in the two cable end, the AC component i larger and at a point it become even larger than the DC component. The quetion i: What hould the minimum difference between the ending and receiving end voltage (amplitude and/or phae angle) be in order to prevent zero-miing phenomenon? There i no definitive anwer to thi quetion, ince it depend on the ytem parameter: Voltage level, cable impedance, cable length, etc. A an example Fig. and Fig. how the minimum value of the difference between the phae angle and the amplitude required to prevent zero-miing phenomenon. For intance, a km cable hould have an energiing voltage with a. pu amplitude difference between the two end or a º phae angle difference. Phae Angle [º].... Length [km] Fig. Minimum difference between phae angle to prevent zero-miing phenomenon for different cable length Amplitude [pu].... Length [km] Fig. Minimum difference between the amplitude to prevent zero-miing phenomenon for different cable length (olid line: V >pu; dahed line; V <pu) V. CONCLUSIONS Zero-miing phenomenon i a non-deirable effect that can occur when energizing cable line with hunt reactor. The phenomenon can lead to the degradation or even detruction of the cable circuit breaker. With the increaing ue of long highvoltage cable, thi problem become more relevant, and countermeaure for it are neceary. Thi paper preent everal countermeaure that can be applied for different condition/ytem, reducing/eliminating zero-miing phenomenon. An analyi of all the countermeaure propoe that two of them be conidered a the mot effective: Connect the hunt reactor when the voltage i at a peak value (when the hunt reactor i connected to the cable through a circuit breaker); Ue of a pre-inertion reitor (when the hunt reactor i connected direct to the cable); If correctly applied thee two countermeaure completely eliminate zero-miing phenomenon, omething that it i not granted when the other countermeaure are applied. A the ytem parameter change from cae to cae, it i alway neceary to analye the ytem to ee which countermeaure hould be applied.

9 IEEE PES Tranaction on Power Delivery Page of TPWD-- BIOGAPHIES APPENDIX A B () + B ( ) V = V + N N () A = LL Cω + ( L Cω + LCω ) + ( Lω + Cω + LL Cω ) + + ( L Cω + LCω + ω ) + () + ( Lω + Cω ) + ω B () = LCω + Cω + + (ω + LCω ) + Cω + ω () B ( ) = LC Lω + ( LC ω + L C ω ) + ( C ω + CLω + LL C ω ) + + ( Cω + L C ω + L C ω ) + () + ( C ω + CLω ) + Cω N = LL Cω + ( L Cω + LCω ) + + ( Lω + Cω ) + ω () EFEENCES [] [] [] [] [] [] [] [] [] [] [] [] [] GE Power Sytem Energy Conulting, "Connecticut Cable Tranient and Harmonic Study for Phae : Final eport", November Tokyo Electric Power Company, "Joint Feaibility Study on the kv Cable Line Endrup-Idomlund: Final eport", April F. Faria da Silva, C. L. Bak, U. S. Gudmunddóttir, W. Wiechowki, M.. Knardrupgård, "Ue of a Pre-Inertion eitor to Minimize ZeroMiing Phenomenon and Switching Overvoltage", IEEE-PES General Meeting, July J. F. Borge da Silva, "Electrotecnia Teórica - ª Parte", nd edition, AEIST, (in Portuguee) J. H.. Enlin, Yi Hu,. A. Wakefield, "Sytem Conideration and Impact of AC Cable Network on Weak High Voltage Tranmiion Network", Tranmiion and Ditribution Conference and Exhibition, / IEEE PES, May Alan Greenwood, "Electric Tranient in Power Sytem", John Wiley & Son, t Edition, Y. H. Fu, G. C. Damtra, "Switching Tranient During Energizing Capacitive Load by a Vacuum Circuit Breaker", IEEE Tranaction on Electrical Inulation, vol. No., pp. -, Augut I. U. S. Hutter, M. Krepela, B. F. Grčić, F. Jakl, Tranient Due to Switching of kv Shunt eactor, International Conference on Power Sytem Tranient (IPST), Brazil, Paper No., June SAGEM, "mm Al XLPE kv dataheet" A. Morched, B. Gutaven, M. Tartibi, "A univeral model for accurate calculation of electromagnetic tranient on overhead line and underground cable," IEEE Tranaction on Power Delivery, (), p., July ABB, "Live Tank Circuit Breaker: Buyer' Guide"; th edition, May M. V. Ecudero, M. edfern, "Effect of tranmiion line contruction on reonance in hunt compenated EHV line", IPST-, June S. Schulz, "Four Lecture on Differential-Algebraic Equation", Humboldt Univerität zu Berlin, June Filipe Faria da Silva wa born in Portugal in and received hi MSc in Electrical and Computer Engineering in from Intituto Superior Técnico (IST), Portugal. He i currently employed with the Danih TSO (Energinet.dk) and doing a PhD at the Intitute of Energy Technology of Aalborg Univerity, where he tudie high-voltage tranmiion ytem with underground cable. Clau Leth Bak wa born in Århu in Denmark, on April,. He tudied at the Engineering College in Århu, where he received the B.Sc. with honor in Electrical Power Engineering in. He purued the M.Sc. in Electrical Power Engineering with pecialization in High Voltage Engineering at the Intitute of Energy Technology (IET) at Aalborg Univerity (AAU), which he received in. After hi tudie he worked with Electric power tranmiion and ubtation with pecialization within the area of power ytem protection at the NV Net tranmiion company. In he got employed a an aitant profeor at IET-AAU, where he i holding an aociate profeor poition today. Hi main reearch area include corona phenomena on overhead line, power ytem tranient imulation and power ytem protection. He i the author/coauthor of app. publication and IEEE Senior Member. Unnur Stella Gudmunddottir wa born in eykjavik in Iceland, in. She received her B.Sc. degree in Electrical and Computer engineering in from The Univerity of Iceland. She tudied for the M.Sc. in Electric Power Sytem at the intitute of Energy Technology, Aalborg Univerity in Denmark and received her degree in with peciality in tate etimation and obervability analyi. She received an honour prie for her M.Sc. final thei. She wa a guet reearcher at SINTEF in Norway in November and at Manitoba HVDC eearch Centre in Canada during June-October. Currently he i tudying PhD at the Intitute of Energy Technology, Aalborg Univerity, in cooperation with the Danih TSO (Energinet.dk), where he alo upervie tudent puruing their M.Sc. degree in energy technology. Her PhD tudie are focued on modelling of underground cable ytem at the tranmiion level. Wojciech Wiechowki received the M.Sc. degree from Waraw Univerity of Technology in and the Ph.D. degree from Aalborg Univerity, Denmark in. From to he worked for HVDC SwePol Link a a Technical Executor. In the period from to he wa with the Intitute of Energy Technology, Aalborg Univerity, firt a a PhD Student and later a an Aitant Profeor. Since he ha been employed in the Planning Department of the Danih TSO Energinet.dk. Hi current reponibilitie include variou power ytem analyi tak related to the planning of the tranmiion network with extenive ue of long AC cable line and wind power generation. He i a Senior Member of IEEE. Martin andrup Knardrupgård wa born in Copenhagen, and received hi M.Sc. E.E. from the Technical Univerity of Denmark. From to he worked for the Swedih electric power company Sydkraft/E.ON where he wa involved in the planning of the regional tranmiion grid in outhern Sweden. Since he joined the planning department of the Danih TSO Energinet.dk. Hi current reponibilitie include long term planning of the Danih tranmiion grid, epecially interconnection with UCTE and Nordel, apect and feaibility tudie of kv cabling and the connection of the offhore wind farm Horn eef, ødand and Anholt.