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954 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS VOL 7 NO 5 SEPTEMBER 2021 Comparison of Costeffective Distances for LFAC with HVAC and HVDC in Their Connections for Offshore and Remote Onshore Wind Energy Xin Xiang Member IEEE Shiyuan Fan Yunjie Gu Senior Member IEEE Wenlong Ming Member IEEE Jianzhong Wu Member IEEE Wuhua Li Member IEEE Xiangning He Fellow IEEE and Timothy C Green Fellow IEEE AbstractFor a costeffective connection of largescale long distance wind energy a low frequency alternating current LFAC transmission scheme 167 Hz or 20 Hz is proposed as an alterna tive to the conventional high voltage alternating current HVAC transmission scheme 50 Hz or 60 Hz and the recently popular high voltage direct current HVDC transmission scheme 0 Hz The technical feasibility of the LFAC system is demonstrated but the basis for identifying the distance ranges for which LFAC would be preferable to HVAC and HVDC are not established and the dependence of this range on factors such as power transfer rating voltage rating and cableline type is not investigated This paper presents an indepth analysis for the overall cost of LFAC system and then provides an extensive comparison with HVAC and HVDC to explore the distance ranges over which LFAC is costeffective over both HVAC and HVDC in connections of offshore and remote onshore wind energy The results demonstrate that the LFAC system does possess ranges in the intermediate distance for which it is more costeffective than both HVAC and HVDC and its overall cost advantage is generally larger in the overhead line OHL connection of remote onshore wind energy than the cable connection of offshore wind energy Index TermsCosteffective ranges LFAC overall cost analysis wind energy NOMENCLATURE A Acronyms C Overall Cost CC Capital Cost CBC Cable Cost CPC Compensation Cost Manuscript received December 27 2020 revised March 2 2021 accepted April 7 2021 Date of online publication April 30 2021 date of current version July 2 2021 This work was supported by the National Natural Science Foundation of China 51925702 52107214 and ChinaUK NSFCEPSRC Joint Project 52061635101 EPT0217801 X Xiang S Y Fan W H Li corresponding author email woohualee zjueducn ORCID httpsorcidorg0000000203455815 and X N He are with the College of Electrical Engineering Zhejiang University Hangzhou 310027 China Y J Gu is with the Department of Electronic and Electrical Engineering University of Bath Bath BA2 7AY UK W L Ming and J Z Wu are with the School of Engineering Cardiff University CF24 3AA Cardiff UK T C Green is with the Department of Electrical and Electronic Engineering Imperial College London London SW7 2AZ UK DOI 1017775CSEEJPES202007000 CSC Current Source Converter FFTS Fractional Frequency Transmission System HVAC High Voltage Alternating Current HVDC High Voltage Direct Current LC Power Losses Cost LFAC Low Frequency Alternating Current OHC Overhead Line Cost OHL Overhead Line RC Route Cost RCC Route Capital Cost RLC Route Power Losses Cost RMS Root Mean Square TC Terminal Cost TCC Terminal Capital Cost TLC Terminal Power Losses Cost VSC Voltage Source Converter B Constants BC Base cost for VSCHVDC offshore platform and plant 25 M BT Base cost for HVAC offshore platform and plant 5 M E Energy average price 50 MWh F Power factor of HVAC system 10 fTC Cost factor of transformer number or converter number per platform 02 QCoff Offshore compensation cost 0025 MMvar QCons Onshore compensation cost 0015 MMvar Tp Project time 15 years VC Variable cost for VSCHVDC offshore platform and plant 0109 MMVA VT Variable cost for HVAC offshore platform and plant 0045 MMVA δop Operation factor 0231 ϑoffT Offshore HVAC transformer plant efficiency 994 ϑoffC Offshore VSCHVDC converter plant rectifier with transf efficiency 9828 ϑonsT Onshore HVAC transformer plant efficiency 994 ϑonsC Onshore VSCHVDC converter plant inverter with transf efficiency 9819 20960042 2020 CSEE XIANG et al COMPARISON OF COSTEFFECTIVE DISTANCES FOR LFAC WITH HVAC AND HVDC IN THEIR CONNECTIONS FOR OFFSHORE AND REMOTE ONSHORE WIND ENERGY 955 ϑonsCSC Onshore CSCHVDC converter plant inverter with transf efficiency 9912 C Variables C Subsea cable shunt capacitance per kilometer Fkm cC Subsea cable cost per set including supply and installation kkm co Onshore OHL cost per set including supply and installation kkm fn Operation frequency Hz Ich Capacitive charging current in subsea cable kA Icn Subsea cable nominal current kA Ion Onshore OHL nominal current kA IQoff Offshore compensation current kA L Onshore OHL series inductance per kilometer Hkm lc Subsea cable length km lo Onshore OHL length km nC HVAC transformer number per platform nT VSCHVAC converter number per platform ncC Number of subsea cable parallel circuits nco Number of Onshore OHL parallel circuits Pc Active power transfer capability in subsea cable MW Po Active power transfer capability in onshore OHL MW Pstl Stability limit in onshore OHL MW Pthl Thermal limit in onshore OHL MW Qc Reactive power produced by capacitive charging current Mvar Qoff Offshore compensation power Mvar Qons Onshore compensation power Mvar rC Subsea cable resistance per kilometer Ωkm ro Onshore OHL resistance per kilometer Ωkm SC Apparent power in subsea cable MVA STT Power transfer rating MVA Vcn Subsea cable nominal voltage kV Von Onshore OHL nominal voltage kV Xo Onshore OHL series reactance per kilometre Ωkm I INTRODUCTION W IND is regarded as one of the most important renew able energy resources throughout the world 13 The total penetration of wind generation in some countries has already exceeded 20 of their total capacity 4 It has also been determined that wind resources are often best installed in offshore or remote onshore areas 5 6 For instance the offshore wind farm generation in Europe is approaching 25 GW as of 2020 and is planned to reach 70 GW by 2030 7 and the largest wind farm station in the world which is located in Jiuquan China remote onshore area has already reached 10 GW capacity 8 These largescale wind farms are usually far away from the metropolitan load centers and this fact has prompted a greater effort to advancing costeffective long distance transmission technologies in connection with wind energy 9 10 High voltage alternating current HVAC and high voltage direct current HVDC systems illustrated in Fig 1 and Fig 2 have been commercialized for this use in both subsea cable form in connection with offshore wind energy and overhead line OHL form in connection with remote onshore wind energy 1114 The overall cost of a wind energy connection system is usually partitioned into the terminal cost and route cost for analysis and comparison 1518 A HVAC system has the advantage of relatively inexpensive terminal costs whereas a HVDC system has an expensive power converter plant at each terminal The route cost in a HVAC system rises much more sharply with distance than that in a HVDC system because of the different transmission capability limits in the AC and DC use of cables and OHL Over short distances a HVAC system is favored for its lower terminal costs but beyond some threshold distance the advantages of lower route costs favors the HVDC system The crossover distance for the overall cost of HVAC and HVDC systems is reported to be in the region of 80 km 1921 for a subsea cable system and 700 km for a remote onshore OHL system 22 23 However the technology choice for HVAC or HVDC on a distance basis is not yet definitive For example the very recent practical wind farm projects of Hornsea 24 25 and Dogger Bank 26 27 made different choices Hornsea chose HVAC while Dogger Bank chose HVDC although they are located in the same area of the North Sea with almost the same power rating This could raise a general equation whether there exists a third technology choice with cost advantages over both HVAC and HVDC for some distance ranges which may further lower the wind energy price and increase wind energy penetration in the future The low frequency alternating current LFAC system 28 30 or alternatively fractional frequency transmission sys tem FFTS 3134 was proposed in the 1990 s and its structure for a wind energy connection is shown in Fig 3 The operational frequency in a LFAC system is usually set at 167 Hz or 20 Hz which is one third of the standard system frequency 50 Hz or 60 Hz for HVAC Because of the lower frequency although the transformer volume tends to increase Stepup Transformer 5060 Hz Stepdown Transformer Generator Centre Load Centre Sending End Receiving End HVAC System Fig 1 Structure of HVAC system 956 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS VOL 7 NO 5 SEPTEMBER 2021 Stepup Transformer Stepdown Transformer HVDC System 0 Hz ACDC DCAC Sending End Generator Centre Receiving End Load Centre Fig 2 Structure of HVDC system LF Stepup Transformer 16720 Hz Stepdown Transformer LFAC System ACAC Generator Centre Sending End Load Centre Receiving End Fig 3 Structure of LFAC system a LFAC system suffers less effects from cable shunt capacitive susceptance or OHL series inductive reactance than a standard HVAC system and so it makes for a more costeffective use of the cable or OHL In the case of a wind farms connection only one ACAC power converter plant is required as an interface between the LFAC system and the standard electrical network to realize frequency conversion Therefore the LFAC system could incur lower terminal costs compared to a HVDC system and the maintenance costs would also be significantly reduced with the removal of an offshore converter station Moreover the voltage stability would be improved since the sensitivity of voltage on reactive power variations is diminished in a LFAC system 35 Furthermore a multiterminal wind energy system could be built relying on LFAC since the protection scheme inherited from the HVAC system has been maturely designed which is difficult to realize with a HVDC system due to the lack of costeffective DC breakers The technical feasibility of a LFAC system has been intensively studied 35 38 over the last decade and a laboratory prototype of a LFAC system has also been successfully demonstrated 39 40 Cost analysis and comparisons for a LFAC system also received some attention 4143 in recent years but not to the degree needed to properly estimate its costeffective distance ranges 4446 in connection with wind energy It is postulated that a LFAC system would have a lower cost than either HVAC or HVDC systems for some intermediate range of distances straddling the threshold distance between HVAC and HVDC This is on the basis that a single power converter at one end will provide a lower terminal cost than an HVDC system but higher than an HVAC system and better cable or OHL use will give a lower route cost than an HVAC system but higher than an HVDC system 4648 Figure 4 illustrates the overall cost against distance for HVAC HVDC and three possible cases of LFAC systems Although all the LFAC cases have terminal costs and unit route costs between those of HVAC and HVDC systems whether the distance range that exists with the optimal choice of LFAC would also be affected by the power ratings and connection forms has not been determined In cases 1 and 2 the overall cost of LFAC crosses the overall cost of HVAC before crossing the Transmission Distance HVDC 0 HZ HVAC 5060Hz LFAC 3 16720Hz Overall Cost LFAC 2 16720Hz LFAC 1 16720Hz HVAC Terminal HVDC Terminal HVAC Route HVDC Route LFAC Terminal LFAC Route Fig 4 Three basic possibilities for LFAC overall cost overall cost of HVDC and so the LFAC system has a cost effective range over which it is cheapest However in case 3 the overall cost of LFAC first crosses the overall cost of HVDC and then there is no distance for which it is the preferred choice Therefore knowing that the terminal costs and unit route costs of the LFAC system lie between those of the HVAC and HVDC systems is not sufficient to establish whether a LFAC scheme has or has not the costeffective range let alone identifying the costeffective distance range for different power ratings with different connection forms A careful analysis of the overall cost of a LFAC system is required and a thorough comparison with HVAC and HVDC is also needed to bridge this knowledge gap which can make a good contribution in the future choice of costeffective technology in connection with largescale offshore and remote onshore wind energy So far few studies have illustrated the cost estimation for the LFAC based wind energy transmission system In this paper an indepth analysis for the overall cost of a LFAC system is presented and an extensive comparison with HVAC and HVDC is further provided to allow estimation of the costeffective distance ranges of LFAC over both HVAC and HVDC in connection with offshore and remote onshore wind energy First the overall cost of a LFAC system is decomposed XIANG et al COMPARISON OF COSTEFFECTIVE DISTANCES FOR LFAC WITH HVAC AND HVDC IN THEIR CONNECTIONS FOR OFFSHORE AND REMOTE ONSHORE WIND ENERGY 957 into constituent parts of terminal and route costs and further decomposed into capital and operational costs Then detailed analysis of each constituent cost follows with a derivation of equations specific to a LFAC system and cost parameters are estimated from the most similar equipment used in HVDC and HVAC projects since there is an absence of commercial LFAC projects that can provide cost data Lastly the cost estimation process considers different choices of operating voltage and numbers of parallel conductors for each distance in order to meet the specified power transfer at minimum cost and finally provide a fair comparison for these three connection systems The results demonstrate that a LFAC system does possess a costeffective distance range over HVAC and HVDC systems in the intermediate distance for both connections of offshore and remote onshore wind energy and its overall cost advantage is generally larger in the OHL connection of remote onshore wind energy than the cable connection of offshore wind energy II DECOMPOSITION OF OVERALL COST An allinclusive analysis of overall cost for a largescale and longdistance wind energy connection system is complex to conduct in analytical form since many detailed practical factors in the system would need to be taken into consideration and the analysis would become intractable 15 21 For a new technology choice such as a LFAC system this is complicated by the absence of fullscale demonstration projects which will have resolved some of the implementation details and established design limits To make the overall cost analysis both feasible and widely applicable some minor factors in the whole connection system have to be neglected 18 49 50 and the cost data of individual items needs to be estimated in broad terms from whatever real practical projects provide a reasonably close data point 51 52 It is common to separate out the terminal cost TC and route cost RC as the major factors in an estimation of the overall cost C for a wind energy connection system The terminal cost is independent of distance while the route cost is a function of distance Table I lists the cost of each constituent of HVAC HVDC and LFAC systems under the headings of TC and RC with reference to Fig 1Fig 3 The descriptions are for an offshore cable connection case with alternative descriptions for a remote onshore OHL connection case given in brackets The overall cost C of a wind energy connection system can also be separated into capital cost CC and the capitalized cost of operational power losses LC The capital cost is relevantly independent of system operational years while power loss cost is a function of operational years Thus the overall cost could be further decomposed as terminal capital cost TCC terminal power loss cost TLC route capital cost RCC and route power loss cost RLC Fig 5 shows these two decomposition directions and illustrates the relevant relationships between these constituent costs and each constituent cost will be discussed and analyzed in detail in the next two sections III ANALYSIS AND ESTIMATE OF THE COSTEFFECTIVE RANGE FOR OFFSHORE CABLE CONNECTIONS By interpreting each constituent cost in Table I for off shore cable connections in terms of Fig 5 reveals that TCC consists of the offshore platform and plant cost TCCoff and onshore plant cost TCCons TLC consists of offshore plant power loss cost TLCoff and onshore plant power loss cost TLCons RCC consists of the cable cost CBC and compensation cost CPC and RLC is the subsea cable power loss cost C CC LC TC TCC TLC RC RCC RLC Sum Sum Fig 5 Decompositions and relationships between constituent costs The cost analysis for each constituent in the two established technologies HVAC and HVDC systems can draw on the TABLE I DECOMPOSITION OF OVERALL COSTS IN HVAC LFAC AND HVDC SYSTEMS FOR OFFSHORE CABLE CONNECTIONS WITH VARIATIONS FOR REMOTE ONSHORE OHL CONNECTIONS IN BRACKETS System Terminal cost TC Route cost RC Terminal Capital Cost TCC Terminal Power Losses Cost TLC Route Capital Cost RCC Route Power Losses Cost RLC HVAC Offshore remoteend stepup transformer plant and platform compound Onshore loadend stepdown transformer plant and compound Cables or OHL and compensation Offshore remoteend transformer plant power losses Onshore loadend transformer plant power losses Cables or OHL power losses HVDC Offshore remoteend converter plant and platform compound including valves transformers and filters Onshore loadend converter plant including valves transformers and filters Cables or OHL Offshore remoteend ACDC converter plant power losses Onshore loadend DCAC converter plant power losses Cables or OHL power losses LFAC Offshore remoteend LF stepup transformer plant and platform compound Onshore loadend ACAC converter plant including valves transformers and filters Cables or OHL and compensation Offshore remoteend LF transformer plant power losses Onshore loadend ACAC converter plant power losses Cables or OHL power losses published estimation methods and practical cost data This also serves as an important starting point for the analysis and estimation for the LFAC system It should be noted that voltagesourceconverter HVDC VSCHVDC is the preferred DC option in connection with offshore wind energy so that an isolated AC grid can be formed for the wind turbines A Cost Analysis and Estimate in HVAC and VSCHVDC Systems Examining cost data obtained from commercial projects shows that the terminal capital cost for HVAC and VSC HVDC systems can be approximately estimated by the empirical formula as in 14 5256 For ease of reference the descriptions for all the variables and relatively assumed values in this paper have been summarized in the Nomenclature section and all the variables will also be described after the specific equation for clarification TCCoffHVAC BT 1 fT nT 2 VT STT 1 TCConsHVAC 002621STT07513 2 TCCoffVSCHVDC BC 1 fC nC 2 VC STT 3 TCConsVSCHVDC 008148STT 4 where BT and BC are the base costs for HVAC and VSC HVDC offshore platform and plant VT and VC are the variable costs for HVAC and VSCHVDC offshore platform and plant nT and nC are the HVAC transformer number and VSC HVDC converter number per platform fT and fC are the cost factors for transformer number and converter number per platform STT is the transfer power rating The capitalized cost of power loss is an accumulated value over an operational time and dependent on an energy price The power loss cost of the offshore plant and onshore plant for HVAC and HVDC systems are calculated by 58 respectively 5761 TLCoffHVAC STT F 1 ϑoffT Tpδop E 5 TLConHVAC STT F ϑoffT ϑCHVAC 1 ϑonsT δop 6 TLCoffVSCHVDC STT F 1 ϑoffC Tpδop E 7 TLConsVSCHVDC STT F ϑoffCϑCVSCHVDC 1 ϑonsC Tpδop E 8 where F is the power factor for transmission ϑoffT and ϑonsT are the efficiencies of an offshore and onshore HVAC transformer plant ϑoffC and ϑonsC are the efficiencies of an offshore VSCHVDC converter plant rectifier with transformer and onshore VSCHVDC converter plant inverter with transformer ϑCHVAC and ϑCVSCHVDC are the efficiencies of HVAC and VSCHVDC cables Top is the project time δop is the operational factor and E is the energy average price Combining 1 2 5 6 and 3 4 7 8 with the assumption values listed in the Nomenclature the terminal cost of the HVAC and VSCHVDC systems are estimated as 9 and 10 respectively TCHVAC TCCHVAC TLCHVAC TCCoffHVAC TCConsHVAC TLCoffHVAC TLConsHVAC 5 0045STT 002621STT07513 000911STT 000906STTϑCHVAC 9 TCVSCHVDC TC CVSCHVDC TLCV SCHVDC TCCV SCHVDC TLCoffVSCHVDC TLConsVSCHVDC 25 011STT 008148STT 002610STT 002701STTϑCVSCHVDC 10 To estimate the cable cost and compensation cost in a standard HVAC system the cable transmission capability needs to first be analyzed Shunt capacitive susceptance is the key parameter limiting active power transfer in a subsea cable and the reactive power produced by capacitive charging current is expressed as 11 Qc 3Vcn32 2πfn C lc Vcn2 2πfn C lc 11 where Qc is the reactive power Vcn is the subsea cable nominal voltage fn is the operational frequency C is the subsea cable shunt capacitance per kilometre and lc is the subsea cable length Splitting the reactive power compensation evenly between the two ends of the subsea cable makes available most of the capacity for active power use 21 51 62 63 On this basis the cable transmission capability is given by 12 and the compensation cost in the HVAC system can be estimated by 13 With the distance increasing the cable transmission capability in the HVAC system will decrease and the required compensation power and compensation cost will increase Pc Sc2 Qoff2 Sc2 Qc22 12 3 Vcn Icn2 14Vcn2 2πfn C lc2 CPCHVAC QCoff QoffHVAC QCons QonsHVAC QCoff QcHVAC2 QCons QcHVAC2 QCoff QCons2 Vcn2 2πfn C lc 13 where Pc is the active power transfer capability in the subsea cable Sc is the apparent power in the subsea cable Qoff is the offshore compensation power Icn is the subsea cable nominal current QCoff and QCons are the offshore and onshore compensation costs Qoff and Qons are the offshore and onshore compensation powers The parameters of the common cables for a HVAC system are listed in Appendix Table I The capital costs and power loss costs of HVAC cables are calculated by 14 and 15 respectively and its efficiency in transmission is expressed in 16 CBCHVAC cc lc ncc 14 RLCHVAC 3STT F ϑoffT ncc 3 Vcn32 rc lc ncc TpδopE STT F ϑoffT Vcn2 rc lc ncc TpδopE 15 STT F ϑoffT STT F ϑoffT Vcn2 rc lc ncc ϑCHVAC S TT F ϑoffT rc lc ncc 16 where cc is the subsea cable cost per set including supply and installation ncc is the number of subsea cable parallel circuits rc is the subsea cable resistance per kilometer A VSCHVDC system has an advantage in active power transfer over HVAC since a DC system can utilize the peak value of voltage continuously whereas the rootmeansquare RMS value of voltage that sets the AC power is a factor of 2 less than the peak value Moreover there is no capacitive shunt current in the DC cable transmission which enlarges the advantages in active power transfer for smaller cable cost and also avoids the compensation cost The parameters of the common VSCHVDC cables are listed in Appendix Table II and 14 can also be used to calculate the cable capital cost The power loss cost of VSC HVDC cables and its efficiency in transmission are given in 17 and 18 RLCVSCHVDC 2STT F ϑoffC ncc 2 Vcn2 rc lc ncc TpδopE STT F ϑoffC Vcn2 rc lc 2ncc TpδopE 17 ϑCVSCHVDC STT F ϑoffC STT F ϑonMC Vcn2 rclc2ncc STT F ϑoffC 1 STT F ϑoffC Vcn2 rc lc 2ncc 18 Combining 1416 and 17 18 with the assumption values in the Nomenclature the route costs of HVAC and VSCHVDC systems are estimated as shown in 19 and 20 respectively RCHVAC RCCHVAC RLCHVAC CBCHVAC CPCHVAC RLCHVAC cc lc ncc 002Vcn2 2π fn C lc 151767 0994 STT Vcn2 rc lc ncc 19 RCVSCHVDC RCCVSCHVDC RLCVSCHVDC CBCVSCHVDC RLCVSCHVDC cc lc ncc 075884 0983STTVcn2 rc lc ncc 20 With 9 10 and 19 20 the estimations of the overall costs for HVAC and VSCHVDC systems are obtained as shown in 21 and 22 CHVAC TCHVAC RCHVAC 5 0045STT 002621STT07513 000911STT 000906 STT 0994STT2 Vcn2 rc lc ncc cc lc ncc 002Vcn2 2πfn C lc 151767 0994STT Vcn2 rc lc ncc 21 CVSCHVDC TCVSCHVDC RCVSCHVDC 25 011STT 008148STT 002610STT 002701 STT 0492STT2 Vcn2 rc lc ncc cc lc ncc 075884 0983STT Vcn2 rc lc ncc 22 standard transformer efficiency For the efficiency of the onshore ACAC converter practical efficiency data of a thyristorbased DCAC converter in a CSCHVDC system 59 79 could be used based on the same analysis for 24 With these assumptions and relative efficiency data given in the Nomenclature the terminal cost estimation for a LFAC system is presented in 25 TCLFAC TCCLFAC TLCLFAC TCCoffLFAC TCConsLFAC TLCoffLFAC TLConsLFAC 53 00453STT 005926STT 000911STT 001303STT ϑCLFAC 25 For the compensation cost in a LFAC system it can be seen in 11 that the reactive power produced by charging current is proportional to the operational frequency and so the required compensation power and compensation cost in a LFAC system will be theoretically one third of that in a HVAC system based on the analysis in 13 The unit price of the subsea cable for a LFAC system is assumed to be the same as the same physical cable for a HVAC system but because of the reduced charging current and skin effect in the cable it will have a larger transmission capability in a LFAC system than in a HVAC system The results of a simulation and experiment 36 8082 on subsea cables identified parameters for a LFAC system are presented in Appendix Table III The cable capital cost power loss cost and cable efficiency calculation can follow the formulas in 1416 with the corresponding parameter adjustments for a LFAC system and its route cost estimation is given as 26 RCLFAC RCCLFAC RLCLFAC CBCLFAC CPCLFAC RLCLFAC cc lc ncc 002 Vcn2 2πfn C lc 151767 0994 STT Vcn2 rc lc ncc 26 With 25 and 26 the estimation of the overall cost for LFAC system is obtained in 27 CLFAC TCLFAC RCLFAC 53 00453STT 000911STT 001303 STT 0994STT2 Vcn2 rc lc ncc cc lc ncc 002Vcn2 2πfn C lc 151767 0994STT Vcn2 rc lc ncc 27 and Appendix Table III for a LFAC system The analysis in 6 shows that the transmission capability of a HVAC or a LFAC cable system will fall off with the increasing distance This is illustrated in Fig 6 with the cable parameters in Appendix Table I and Appendix Table III It can be seen in Fig 6 that a LFAC system has a significant advantage over a HVAC system in terms of usable distance of a given cable based on the reduction in charging current and skin effect For a HVDC scheme where charging current and reactive power do not apply the cable transmission capability would not decrease with the increasing distance and so a given cable can be used over any distance for its rated transfer power Fig 6 Transmission capability of some common cables in HVAC and LFAC with even compensation in both ends XIANG et al COMPARISON OF COSTEFFECTIVE DISTANCES FOR LFAC WITH HVAC AND HVDC IN THEIR CONNECTIONS FOR OFFSHORE AND REMOTE ONSHORE WIND ENERGY 961 TABLE II CABLE CHOICES FOR 06 GW CONNECTION CASE System Distance km Voltage kV Size mm2 Capability per circuit GW Number of circuits nc HVAC 065 400 1000 06460604 1 6580 400 1400 06390603 1 80120 220 800 03200300 2 120150 220 1000 03210299 2 150200 220 630 02550205 3 200215 220 800 02250203 3 215230 132 800 01580150 4 230240 132 1000 01570151 4 LFAC 0240 400 800 07330685 1 VSCHVDC 0240 300 1000 0986 1 0 20 40 60 80 100 120 Transmission Distance lc km 140 160 180 200 220 240 0 250 500 750 1000 1250 Overall Cost M 376 Mkm 04 GW P2 03GW P1 353 Mkm 337 Mkm 283 Mkm 238 Mkm 234 Mkm 209 Mkm 178 Mkm 4610 M C TC Fig 7 Overall cost estimate of a 06 GW HVAC system P1 03 GW CapriTorre Annunziata Interconnector in Italy P2 04 GW Kriegers Flak Combined Grid Interconnector between Denmark and Germany 0 20 40 60 80 100 120 Transmission Distance lc km 140 160 180 200 220 240 0 250 500 750 1000 1250 Overall Cost M RCC TCC TLC RLC Fig 8 Constituent costs of a 06 GW HVAC system Cost estimation for 06 GW VSCHVDC offshore cable connection were produced from 20 and plotted in Fig 9 The terminal cost is 171 8 M and the route cost per unit distance maintains the same value at 092 Mkm for all distances up to 240 km The detailed constituent costs are recorded in Fig 10 and Appendix Table V Cost data for three commercial and comparable connections the 10 GW ElecLink Interconnector between UK and France the 07 GW Kontek2 Interconnector between Denmark and Germany and the 06 GW ELMED Interconnector between Italy and Tunisia were obtained 92 95 and plotted as P1 P2 and P3 respectively in Fig 9 which provides reassurance for the overall cost estimation of a VSC 0 20 40 60 80 100 120 140 160 180 200 220 240 0 250 500 750 1000 1250 Overall Cost M 10GW P1 17180 M 092 Mkm 07GW P2 06 GW P3 C TC Transmission Distance lc km Fig 9 Overall cost estimate of a 06 GW VSCHVDC system P1 1 GW ElecLink Interconnector between UK and France P2 07 GW Kontek2 Interconnector between Denmark and Germany P3 06 GW ELMED Inter connector between Italy and Tunisia 0 20 40 60 80 100 120 Transmission Distance lc km 140 160 180 200 220 240 0 250 500 750 1000 1250 Overall Cost M RCC TCC TLC RLC Fig 10 Constituent costs of a 06 GW VSCHVDC system HVDC system The cost estimation for a LFAC system based on 25 are presented in Fig 11 Fig 12 and Appendix Table VI The terminal cost is 104 2 M and the route cost per unit distance is maintained at 151 Mkm for all distances up to 240 km There are no practically realized LFAC offshore connections to use for validation However the costs of individual items were estimated from similar HVAC and HVDC items and these were partially validated in the comparisons of Fig 7 and Fig 9 Comparison results of these three technologies are provided in Fig 13a for the distance ranges 0240 km and a detailed view of the ranges 65125 km given in Fig 13b It can 962 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS VOL 7 NO 5 SEPTEMBER 2021 0 20 40 60 80 100 120 Transmission Distance lc km 140 160 180 200 220 240 0 250 500 750 1000 1250 Overall Cost M C TC 10420 M 151 Mkm Fig 11 Cost estimate of a 06 GW LFAC system 0 20 40 60 80 100 120 Transmission Distance lc km 140 160 180 200 220 240 0 250 500 750 1000 1250 Overall Cost M RCC TCC TLC RLC Fig 12 Constituent costs of a 06 GW LFAC system be seen that the overall cost of a LFAC system crosses the overall cost of a HVAC system at 80 km before crossing the overall cost of HVDC at 115 km giving a range of 35 km over which LFAC is the leastcost solution and the percentage of overall cost advantage over both HVAC and HVDC is about 10 in this case The terminal cost of a LFAC system is approximately halfway between that of the HVAC and HVDC systems The route cost per unit distance of a HVAC system changes several times as the cable choice changes but beyond 65 km the route of a LFAC system lies closer to a HVDC system than to a HVAC system and this condition corresponds 0 20 40 60 80 100 120 Transmission Distance lc km 140 160 180 200 220 240 0 250 500 750 1000 1250 Overall Cost M HVAC VSCHVDC LFAC 65 70 75 80 85 90 95 Transmission Distance lc km 100 105 110 115 120 125 200 225 250 275 300 325 Overall Cost M HVAC VSCHVDC LFAC 35 km a b Fig 13 06 GW overall cost comparison among HVAC VSCHVDC and LFAC system a Full distance comparison b Detailed view for the cross over and breakeven points to the cases 1 and 2 in Fig 4 The crossover point of HVAC and VSCHVDC costs is at 87 km which is close to the value expected given the commercial project data available 1921 and gives reassurance that the cost curves are realistic D Case Study for Higher Power Rating Connection A wind power connection of 14 GW was chosen for the higher power rating case study The minimumcost choices of cable for each of the three schemes are recorded in Table III The estimated overall cost and their constituent costs of each connection technology are plotted in Fig 14Fig 19 and the TABLE III CABLE CHOICES FOR 14 GW CONNECTION CASE System Distance km Voltage kV Size mm2 Capability per circuit GW Number of circuits nc HVAC 030 400 1600 07180703 2 3050 400 2000 07320703 2 50115 400 800 05800471 3 115130 400 1000 05030458 3 130150 220 800 02940280 5 150170 220 800 02970279 5 170195 220 800 02600232 6 195215 220 800 02320203 7 215230 220 800 02030176 8 230240 132 800 01500145 10 LFAC 0200 400 800 07330685 2 200240 400 1000 07490733 2 VSCHVDC 0240 300 2000 1444 1 XIANG et al COMPARISON OF COSTEFFECTIVE DISTANCES FOR LFAC WITH HVAC AND HVDC IN THEIR CONNECTIONS FOR OFFSHORE AND REMOTE ONSHORE WIND ENERGY 963 detailed cost data are given in Appendix Table VIIAppendix Table X 0 20 40 60 80 100 120 Transmission Distance lc km 140 160 180 200 220 240 0 500 1000 1500 2000 2500 Overall Cost M 873 Mkm 844 Mkm 745 Mkm 647 Mkm 551 Mkm 498 Mkm 473 Mkm 453 Mkm 9750 M 523 Mkm 560 Mkm C TC Fig 14 Overall cost estimate of a 14 GW HVAC system 0 20 40 60 80 100 120 Transmission Distance lc km 140 160 180 200 220 240 0 500 1000 1500 2000 2500 Overall Cost M RCC TCC TLC RLC Fig 15 Constitute costs of a 14 GW HVAC system 0 20 40 60 80 100 120 140 160 180 200 220 240 0 500 1000 1500 2000 2500 Overall Cost M 36640 M 131 Mkm C TC Transmission Distance lc km Fig 16 Overall cost estimate of a 14 GW VSCHVDC system The comparison result for the three technologies is provided in Fig 20a over distances from 0240 km and are shown in detail over 6589 km in Fig 20b The crossover points of a LFAC system with HVAC and VSCHVDC are 67 km and 79 km respectively which straddle the crossover point of HVAC and VSCHVDC costs at 73 km for this higher 0 20 40 60 80 100 120 Transmission Distance lc km 140 160 180 200 220 240 0 500 1000 1500 2000 2500 Overall Cost M RCC TCC TLC RLC Fig 17 Constituent costs of a 14 GW VSCHVDC system 0 20 40 60 80 100 120 140 160 180 200 220 240 0 500 1000 1500 2000 2500 Overall Cost M 313 Mkm 335 Mkm 23470 Mkm C TC Transmission Distance lc km Fig 18 Cost analysis of a 14 GW LFAC system 0 20 40 60 80 100 120 Transmission Distance lc km 140 160 180 200 220 240 0 500 1000 1500 2000 2500 Overall Cost M RCC TCC TLC RLC Fig 19 Constituent costs of a 14 GW LFAC system power rating comparison It is clear that the costeffective range and overall cost advantage in the intermediate distance for a LFAC system is narrower at 14 GW than it was at 06 GW in Fig 13 The terminal cost of a LFAC system is closer to that of a HVDC than HVAC system and its route cost per unit distance lies above halfway between HVDC than HVAC in the intermediate range from 50 km to 115 km With reference to Fig 4 at this higher power rating case study the overall cost of LFAC starts to move from the cases 1 and 2 toward case 3 Appendix Table XI and the route cost for an OHLbased CSCHVDC system is given by 33 based on 14 and 17 RCCSCHVDCRCCCSCHVDCRLCCSCHVDCcolonco0758840991STTVon2rolonco 33 Summing the terminal costs and route costs yields the estimates of overall costs Adding 28 and 32 gives 34 for a HVAC system and adding 29 and 33 gives 35 for a CSCHVDC system CHVACTCHVACRCHVAC2002621STT07513000911STT000906STT0994STT2Von2roloncocolonco1517670994STTVon2rolonco 34 CCSCHVDCTCCSCHVDCRCCSCHVDC2005926STT001331STT001319STT0496STT2Von2roloncocolonco0758840991STTVon2rolonco 35 B Cost Analysis and Estimate in a LFAC System Building on the analysis in 28 and 29 for HVAC and CSCHVDC systems the terminal cost for a LFAC system can be estimated by 36 TCLFACTCCLFACTLCLFACTCCremLFACTCCloaLFACTLCremLFACTLCloaLFAC0026213STT07513005926STT000911STT001323STT0994STT2Von2rolonco 36 For the route cost of LFAC the price per unit distance of the OHL is assumed to be the same as for HVAC but as 31 suggests the stability limit in LFAC is expected to be at a distance three times that of HVAC assuming a frequency reduction to one third The parameters of onshore OHL LFAC can be taken from the simulation and experimental results 39 42 97 and are presented in Appendix Table XII and the route cost for an OHLbased LFAC system is provided in 37 RCLFACRCCLFACRLCLFACcolonco1517670994STTVon2rolonco 37 Adding the terminal cost and route cost of 36 and 37 yields the overall cost for a LFAC system as given in 38 CLFACTCLFACRCLFAC0026213STT07513005926STT000911STT001323STT0994STT2Von2roloncocolonco1517670994STTVon2rolonco 38 C Case Study for Lower Power Rating Connection A wind power connection of 30 GW was selected as an example of a relatively lower power rating case study Following Sections IIIC and IIID the choice of voltage rating and OHL current capacity should be reexamined at each distance for AC schemes and a minimumcost choice can be made from the options available In this study the available OHL are given in Appendix Table X for a HVAC system and Appendix Table XII for a LFAC system According to the analysis in 30 and 31 it is the thermal limit that is relevant for HVAC and LFAC systems applied over short distances and beyond this the stability limit is the constraInternational The changeover distance between the limitations is greater for LFAC than HVAC and this is clear from the results in Fig 21 and with the parameters in Appendix Table X and Appendix Table XII It can be seen that a LFAC system has a clear advantage over a HVAC system due to the reduced impact of skin effect for the thermal limit and the onethird series reactance which extends the stability limit It also illustrates that since the thermal limit is irrelevant to the transmission distance while the reliability limit is relevant the constant transmission capacity over shorter distances and the declining capacity over longer distances can be observed for OHLbased AC schemes For a DC scheme a CSCHVDC system does not suffer from effects of the series inductive reactance and the transmission capability is set by the thermal limit at all distances Fig 21 Transmission capability of some typical OHL in HVAC and L Table IV records the minimumcost choices of OHL made for distances up to 1500 km which is representative of remote onshore wind farm locations 8387 Using the OHL choices in Table IV and the analysis of 32 33 and 36 the estimated overall cost of a 30 GW remote onshore OHL connection via HVAC CSCHVDC and LFAC was calculated over 01500 km The results are plotted Fig 20 14 GW overall cost comparison among HVAC VSCHVDC and LFAC system a Full distance comparison b Detailed view for the crossover and breakeven points 966 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS VOL 7 NO 5 SEPTEMBER 2021 TABLE IV OHL CHOICES FOR 30 GW CONNECTION CASE System Distance km Voltage kV Capability per circuit GW Number of circuits nc HVAC 0645 750 56903007 1 6451290 750 30071504 2 12901500 750 15041293 3 LFAC 01500 750 68193879 2 CSCHVDC 01500 600 6564 1 in Fig 22Fig 27 and further details are provided in Appendix Table XIIIAppendix Table XV 0 150 300 450 600 750 900 1050 1200 1500 0 500 1000 1500 2000 2500 Overall Cost M 121 Mkm 088 Mkm 066 Mkm 9400 M 1350 C TC Transmission Distance lc km Fig 22 Overall cost estimate of a 30 GW HVAC system 0 500 1000 1500 2000 2500 Overall Cost M RCC TCC TLC RLC 0 150 300 450 600 750 900 1050 1200 1350 1500 Transmission Distance lc km Fig 23 Constituent costs of a 30 GW HVAC system The comparison result is given in Fig 28a for the distance from 01500 km and a detailed view of 6001000 km is provided in Fig 28b The crossover points of a LFAC system with HVAC and CSCHVDC are 650 km and 960 km respectively giving a costeffective range of 310 km in the intermediate distance and the overall cost advantage over both HVAC and HVDC is close to 15 in this case study It can be seen that the terminal cost of a LFAC system is approximately midway between that of the HVAC and HVDC systems The route cost is a relatively complex picture because the unit cost of AC increases with distance as the stability limit grows in significance and this happens more so in standard frequency than low frequency For distances below 650 km the route cost per unit distance of LFAC and HVAC are 0 150 300 450 600 750 900 1050 1200 1500 0 500 1000 1500 2000 2500 Overall Cost M 43289 M 039 Mkm 1350 C TC Transmission Distance lc km Fig 24 Overall cost estimate of a 30 GW CSCHVDC system 0 500 1000 1500 2000 2500 Overall Cost M RCC TCC TLC RLC 0 150 300 450 600 750 900 1050 1200 1350 1500 Transmission Distance lc km Fig 25 Constituent costs of a 30 GW HVDC system 0 150 300 450 600 750 900 1050 1200 1500 0 500 1000 1500 2000 2500 Overall Cost M 27248 M 056 Mkm 1350 C TC Transmission Distance lc km Fig 26 Overall cost estimate of a 30 GW LFAC system similar but beyond that the route cost of HVAC rises rapidly as parallel circuits are required whereas a single circuit suffices for LFAC all the way to 1500 km and so the route cost of LFAC lies closer to HVDC than to HVAC after 650 km The overall cost of a LFAC system in this OHLbased lower power connection belongs to a situation between case 1 and case 2 as shown in Fig 4 The breakeven point of HVAC and CSC HVDC is 700 km which reaches good agreement with the practical result in the commercial OHLbased remote onshore connection projects 22 23 XIANG et al COMPARISON OF COSTEFFECTIVE DISTANCES FOR LFAC WITH HVAC AND HVDC IN THEIR CONNECTIONS FOR OFFSHORE AND REMOTE ONSHORE WIND ENERGY 967 0 500 1000 1500 2000 2500 Overall Cost M RCC TCC TLC RLC 0 150 300 450 600 750 900 1050 1200 1350 1500 Transmission Distance lc km Fig 27 Constituent costs of a 30 GW LFAC system 0 150 300 450 600 750 900 1050 1200 1500 0 500 1000 1500 2000 2500 Overall Cost M HVAC CSCHVDC LFAC 1350 600 640 680 720 760 800 840 880 920 1000 575 655 735 815 895 975 Overall Cost M 960 HVAC CSCHVDC LFAC 310 km Transmission Distance lc km b Transmission Distance lc km a Fig 28 30 GW overall cost comparison among HVAC CSCHVDC and LFAC systems a Full distance comparison b Detailed view for the cross over and breakeven points D Case Study for Higher Power Rating Connection A power connection of 50 GW was chosen for the higher power rating case study The minimumcost choices of OHL for each of the three technologies over 01500 km are pre sented in Table V The estimated overall costs of each technology choice at 50 GW connection are plotted in Fig 29Fig 34 and the details of the constituent costs are given in Appendix Table XVI Appendix Table XVIII TABLE V OHL CHOICES FOR 50 GW CONNECTION CASE System Distance km Voltage kV Capability per circuit GW Number of circuits nc HVAC 0775 750 56902503 2 7751164 750 25031666 3 11641500 750 16661293 4 LFAC 01164 750 68194999 1 11641500 750 49993879 2 CSCHVDC 01500 600 6564 1 0 0 600 1200 1800 2400 3000 Overall Cost M 168 Mkm 138 Mkm 114 Mkm 14270 M 150 300 450 600 750 900 1050 1200 1500 1350 C TC Transmission Distance lc km Fig 29 Overall cost estimate of a 50 GW HVAC system 0 600 1200 1800 2400 3000 Overall Cost M RCC TCC TLC RLC 0 150 300 450 600 750 900 1050 1200 1350 1500 Transmission Distance lc km Fig 30 Constituent costs of a 50 GW HVAC system The comparison results are provided in Fig 35a over the whole distance with details over 7501000 km in Fig 35b It shows the crossover points of the LFAC overall cost with HVAC and CSCHVDC are 775 km and 965 km respectively which straddle the crossover point of HVAC and CSCHVDC overall costs at 790 km The costeffective range for LFAC is narrowed to 190 km at this 50 GW comparison whereas it was 310 km at 30 GW comparison and the percentage of overall cost advances is also reduced in this case study In this higher power connection case the terminal cost of a LFAC system is between that of HVAC and HVDC but becomes closer to HVDC The unit route cost per unit distance of LFAC is higher than the midpoint of the HVAC and CSCHVDC systems in the intermediate range and shows one increase at 968 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS VOL 7 NO 5 SEPTEMBER 2021 0 0 600 1200 1800 2400 3000 Overall Cost M 72240 M 064 Mkm 150 300 450 600 750 900 1050 1200 1500 1350 C TC Transmission Distance lc km Fig 31 Overall cost estimate of a 50 GW CSCHVDC system 0 600 1200 1800 2400 3000 Overall Cost M RCC TCC TLC RLC 0 150 300 450 600 750 900 1050 1200 1350 1500 Transmission Distance lc km Fig 32 Constituent costs of a 50 GW CSCHVDC system 0 0 600 1200 1800 2400 3000 Overall Cost M C TC 45910 M 093 Mkm 102 Mkm 150 300 450 600 750 900 1050 1200 1350 1500 Transmission Distance lc km Fig 33 Overall cost estimate of a 50 GW LFAC system 1164 km because of a need to move to two parallel circuits This comparison results belong to a situation between the case 2 and case 3 of Fig 4 V DISCUSSION OF COSTEFFECTIVE DISTANCE The crossover points of overall costs between HVAC HVDC and LFAC in the four case studies of wind energy con nections lower power rating and higher power rating offshore cable connection and remote onshore OHL connection are summarized in Table VI The range of costeffective distance 0 600 1200 1800 2400 3000 Overall Cost M RCC TCC TLC RLC 0 150 300 450 600 750 900 1050 1200 1350 1500 Transmission Distance lc km Fig 34 Constituent costs of a 50 GW LFAC system 0 0 600 1200 1800 2400 3000 Overall Cost M Overall Cost M HVAC CSCHVDC LFAC 150 300 450 600 750 900 1050 1200 1500 1350 750 775 800 825 850 875 900 925 950 975 1000 1050 1150 1250 1350 1450 1550 HVAC CSCHVDC LFAC 190 km Transmission Distance lc km a Transmission Distance lc km b Fig 35 50 GW overall cost comparison among HVAC CSCHVDC and LFAC systems a Full distance comparison of b Detailed view for the crossover and breakeven points for the LFAC system is also recorded First it can be seen that there is indeed a costeffective range for the LFAC system over both HVAC and HVDC technologies in the intermediate distance for all the four cases of wind energy connection Second it can be determined that the costeffective range narrows with increasing power rating for both offshore cable connections and remote onshore OHL connections The nar rowing of the costeffective range with an increasing power rating can be explained by reference to the detailed constituent TABLE VI SUMMARY OF CROSSOVER POINTS AND LFAC COSTEFFECTIVE RANGES Case study Crossover points of overall costs LFAC costeffective ranges LFACHVAC HVDCHVAC HVDCLFAC Cable 06 GW 80 km 87 km 115 km 35 km 145 of full length Cable 14 GW 67 km 73 km 79 km 12 km 50 of full length OHL 30 GW 650 km 700 km 960 km 310 km 207 of full length OHL 50 GW 775 km 790 km 965 km 190 km 127 of full length 970 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS VOL 7 NO 5 SEPTEMBER 2021 power transfer and provide a fair comparison for these three technology choices Graphs of costs against distance for offshore cable and remote onshore OHL cases and for lower and higher power connection cases have been created The results have demon strated that the LFAC system does possess distance ranges over which it is expected to be more costeffective than both HVAC and HVDC systems The overall cost advantage of LFAC is generally larger in the OHL connection of remote onshore wind energy than the cable connection of offshore wind energy and it is more competitive for a lower power rating connection than higher power rating connection in both the cable and OHL cases APPENDIX Appendix TABLE I PARAMETERS OF THE COMMON CABLES IN A HVAC SYSTEM Nominal Voltage Vn kV Cable size mm2 Resistance rc mΩkm Capacitance C nFkm Nominal Current In A Cables cost cc kkm 132 500 493 192 739 635 630 395 209 818 685 800 324 217 888 795 1000 275 238 949 860 220 500 489 136 732 815 630 391 151 808 850 800 319 163 879 975 1000 270 177 942 1000 400 800 314 130 870 1400 1000 265 140 932 1550 1200 221 170 986 1700 1400 189 180 1015 1850 1600 166 190 1036 2000 2000 132 200 1078 2150 Appendix TABLE II PARAMETERS OF THE COMMON CABLES IN A VSCHVDC SYSTEM Nominal Voltage Vn kV Cable size mm2 Resistance rc mΩkm Nominal Current In A Cables cost cc kkm 150 1000 224 1644 670 1200 192 1791 730 1400 165 1962 785 1600 144 2123 840 2000 115 2407 900 220 1000 224 1644 855 1200 192 1791 940 1400 165 1962 1015 1600 144 2123 1090 2000 115 2407 1175 Appendix TABLE III PARAMETERS OF THE COMMON CABLES IN A LFAC SYSTEM Nominal Voltage Vn kV Cable size mm2 Resistance rc mΩkm Capacitance C nFkm Nominal Current In A Cables cost cc kkm 132 500 326 192 899 635 630 262 209 995 685 800 215 217 1080 795 1000 182 238 1154 860 220 500 324 136 890 815 630 259 151 982 850 800 211 163 1069 975 1000 179 177 1145 1000 400 800 208 130 1058 1400 1000 175 140 1133 1550 1200 146 170 1199 1700 1400 125 180 1234 1850 1600 110 190 1260 2000 2000 87 200 1310 2150 Appendix TABLE IV DETAILED CONSTITUENT COST DATA FOR A 06 GW HVAC SYSTEM HVAC Transmission Distance l km 0 20 40 60 80 100 120 140 160 180 200 220 240 Cost M TCC 352 352 352 352 352 352 352 352 352 352 352 352 352 TLC 109 109 109 109 109 108 108 108 108 107 107 106 106 RCC 0 338 676 1014 1625 2167 2600 3121 4300 4938 6400 7205 8506 RLC 0 18 36 54 51 178 214 211 233 262 238 553 512 C 461 817 1173 1529 2137 2805 3274 3793 4993 5659 7097 8216 9476 Appendix TABLE V DETAILED CONSTITUENT COST DATA FOR A 06 GW VSCHVDC SYSTEM HVDC Transmission Distance l km 0 20 40 60 80 100 120 140 160 180 200 220 240 Cost M TCC 1396 1396 1396 1396 1396 1396 1396 1396 1396 1396 1396 1396 1396 TLC 319 319 319 318 318 318 318 318 318 318 318 317 317 RCC 0 171 342 513 684 855 1026 1197 1368 1539 171 1881 2052 RLC 0 13 26 39 53 66 79 92 105 118 132 145 157 C 1715 1899 2083 2266 2451 2635 2819 3003 3187 3371 3556 3739 3922 Appendix TABLE VI DETAILED CONSTITUENT COST DATA FOR A 06 GW LFAC SYSTEM LFAAC Transmission Distance l km 0 20 40 60 80 100 120 140 160 180 200 220 240 Cost M TCC 908 908 908 908 908 908 908 908 908 908 908 908 908 TLC 134 133 134 134 134 133 133 133 133 133 133 133 133 RCC 0 289 577 866 1155 1444 1732 2021 2310 2598 2887 3176 3465 RLC 0 14 28 42 56 70 84 98 112 127 141 155 169 C 1042 1344 1647 1950 2253 2555 2857 3160 3463 3766 4069 4372 4675 XIANG et al COMPARISON OF COSTEFFECTIVE DISTANCES FOR LFAC WITH HVAC AND HVDC IN THEIR CONNECTIONS FOR OFFSHORE AND REMOTE ONSHORE WIND ENERGY 971 Appendix TABLE VII DETAILED CONSTITUENT COST DATA FOR A 14 GW HVAC SYSTEM HVAC Transmission Distance l km 0 20 40 60 80 100 120 140 160 180 200 220 240 Cost M TCC 739 739 739 739 739 739 739 739 739 739 739 739 739 TLC 244 244 244 244 243 243 243 241 241 241 241 241 236 RCC 0 876 1841 2905 3873 4841 6087 7172 8530 11065 14344 18032 19650 RLC 0 31 49 116 154 193 195 543 525 582 554 534 1314 C 995 1902 2885 4016 5021 6028 7276 8707 10047 12639 15890 19558 21951 Appendix TABLE VIII DETAILED CONSTITUENT COST DATA FOR A 14 GW VSCHVDC SYSTEM HVDC Transmission Distance l km 0 20 40 60 80 100 120 140 160 180 200 220 240 Cost M TCC 292 292 292 292 292 292 292 292 292 292 292 292 292 TLC 744 743 743 743 742 742 742 741 741 741 740 740 740 RCC 0 235 470 705 940 1175 1410 1645 1880 2115 2350 2585 2820 RLC 0 37 74 110 147 184 221 257 294 331 368 404 441 C 3664 3935 4207 4478 4749 5021 5293 5563 5835 6107 6378 6649 6921 Appendix TABLE IX DETAILED CONSTITUENT COST DATA FOR A 14 GW LFAC SYSTEM LFAC Transmission Distance l km 0 20 40 60 80 100 120 140 160 180 200 220 240 Cost M TCC 2014 2014 2014 2014 2014 2014 2014 2014 2014 2014 2014 2014 2014 TLC 333 332 332 332 331 331 331 330 330 330 330 330 330 RCC 0 577 1155 1732 2310 2887 3465 4042 4619 5197 5774 7026 7665 RLC 0 38 77 115 153 191 230 268 306 344 383 354 386 C 2317 2931 3548 4163 4778 5393 6010 6624 7239 7855 8470 9694 10362 Appendix TABLE X PARAMETERS OF THE TYPICAL OHL IN A HVAC SYSTEM Nominal Voltage Vn kV 380 500 750 OHL type 562AL149ST1A 494AL134ST1A 653AL145ST1A Aluminium area mm2 2 562 3 494 4 653 Nominal current In A 2100 2850 4380 Resistance ro Ωkm 0029 0022 0012 Reactance Xo Ωkm 033 030 029 OHL cost per circuit co kkm 165 245 370 Appendix TABLE XI PARAMETERS OF THE TYPICAL OHL IN A CSCHVDC SYSTEM Nominal Voltage Vn kV 300 400 600 OHL type 562AL149ST1A 494AL134ST1A 653AL145ST1A Aluminium area mm2 2 562 3 494 4 653 Nominal current In A 2620 3560 5470 OHL cost per circuit co kkm 165 245 370 Appendix TABLE XII PARAMETERS OF THE TYPICAL OHL IN A LFAC SYSTEM Nominal Voltage Vn kV 380 500 750 OHL type 562AL149ST1A 494AL134ST1A 653AL145ST1A Aluminium area mm2 2 562 3 494 4 653 Nominal current In A 2520 3420 5250 Resistance ro Ωkm 0019 0015 00079 Reactance Xo Ωkm 011 010 0097 OHL cost per circuit co kkm 165 245 370 Appendix TABLE XIII DETAILED CONSTITUENT COST DATA FOR A 30 GW HVAC SYSTEM HVAC Transmission Distance l km 0 150 300 450 600 750 900 1050 1200 1350 1500 Cost M TCC 391 391 391 391 391 391 391 391 391 391 391 TLC 555 552 550 547 545 548 547 546 545 547 546 RCC 0 555 111 1665 222 555 666 777 888 14985 1665 RLC 0 433 865 1298 1730 1081 1298 1514 1730 1298 1442 C 926 1911 2896 3881 4866 7550 8876 10201 11526 17204 19009 972 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS VOL 7 NO 5 SEPTEMBER 2021 Appendix TABLE XIV DETAILED CONSTITUENT COST DATA FOR A 30 GW CSCHVDC SYSTEM HVDC Transmission Distance l km 0 150 300 450 600 750 900 1050 1200 1350 1500 Cost M TCC 354 354 354 354 354 354 354 354 354 354 354 TLC 794 794 793 792 791 790 789 788 787 786 785 RCC 0 375 75 1125 150 1875 225 2625 300 3375 375 RLC 0 212 424 636 848 1060 1273 1485 1697 1909 2121 C 4334 4921 5507 6093 6679 7265 7851 8438 9024 9610 10196 Appendix TABLE XV DETAILED CONSTITUENT COST DATA FOR A 30 GW LFAC SYSTEM LFAC Transmission Distance l km 0 150 300 450 600 750 900 1050 1200 1350 1500 Cost M TCC 2090 2090 2090 2090 2090 2090 2090 2090 2090 2090 2090 TLC 650 648 645 643 640 648 645 643 640 638 635 RCC 0 555 111 1665 222 2775 333 3885 444 4995 555 RLC 0 284 569 853 1138 1422 1706 1991 2275 2559 2844 C 2770 3607 4444 5281 6118 6955 7791 8629 9465 10302 11139 Appendix TABLE XVI DETAILED CONSTITUENT COST DATA FOR A 50 GW HVAC SYSTEM HVAC Transmission Distance l km 0 150 300 450 600 750 900 1050 1200 1350 1500 Cost M TCC 557 557 557 557 557 557 557 557 557 557 557 TLC 888 885 881 877 874 870 874 871 874 872 870 RCC 0 111 222 333 444 555 999 11655 1776 1998 2220 RLC 0 601 1201 1802 2403 3004 2403 2803 2403 2703 3004 C 1467 3174 4881 6588 8296 10003 13846 15909 21616 24134 26653 Appendix TABLE XVII DETAILED CONSTITUENT COST DATA FOR A 50 GW CSCHVDC SYSTEM HVDC Transmission Distance l km 0 150 300 450 600 750 900 1050 1200 1350 1500 Cost M TCC 590 590 590 590 590 590 590 590 590 590 590 TLC 1324 1322 1319 1316 1314 1311 1309 1306 1304 1301 1298 RCC 0 375 75 1125 150 1875 225 2625 300 3375 375 RLC 0 589 1178 1767 2357 2946 3535 4124 4713 5302 5891 C 7224 8186 9147 10109 11070 12032 12993 13955 14917 15878 16840 Appendix TABLE XVIII DETAILED CONSTITUENT COST DATA FOR A 50 GW LFAC SYSTEM LFAC Transmission Distance l km 0 150 300 450 600 750 900 1050 1200 1350 1500 Cost M TCC 3467 3467 3467 3467 3467 3467 3467 3467 3467 3467 3467 TLC 1157 1150 1142 1135 1128 1121 1113 1106 1128 1124 1121 RCC 0 555 111 1665 222 2775 333 3885 888 999 1110 RLC 0 833 1667 2500 3334 4167 5000 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International Conference on Advances in Electronics Computers and Communications Bangalore 2014 pp 16 Xin Xiang S17M18 received the BSc degree from Harbin Institute of Technology China in 2011 the MSc degree from Zhejiang University China in 2014 and the PhD degree from Imperial College London UK in 2018 all in Electrical and Electronic Engineering He has received the Eryl Cadwaladr Davies Prize for the Best PhD Thesis of the Electrical and Electronic Engineering Department in the Imperial College London and he was also the recipient of the Best PhD Thesis Award from IEEE PELS UK and Ireland Chapter From 2018 to 2020 he was a Research Associate with the Imperial College London UK He is currently a tenuretrack Associate Professor in the College of Electrical Engineering Zhejiang University China His research interests include the analysis and control of power electronics converters for power system applications Shiyuan Fan received the BSc degree in Electrical Engineering and its Automation from North China Electric Power University Beijing China in 2018 She is currently working toward the PhD degree in Electrical Engineering at Zhejiang University Zhejiang China Her research interests include control of modular multilevel converters Yunjie Gu M16SM20 received the BSc and the PhD degrees in Electrical Engineering from Zhejiang University Hangzhou China in 2010 and 2015 respectively He was a Consulting Engi neer with General Electric Global Research Centre Shanghai China from 2015 to 2016 After that he joined the Imperial College UK under the spon sorship of the UKRI Innovation Fellowship He is currently a Lecturer Assistant Professor with the University of Bath UK and an Honorary Lecturer at the Imperial College His research focuses on the fundamental theories and computational tools for analyzing power system dynamics as well as the algorithms and software for power conversion control XIANG et al COMPARISON OF COSTEFFECTIVE DISTANCES FOR LFAC WITH HVAC AND HVDC IN THEIR CONNECTIONS FOR OFFSHORE AND REMOTE ONSHORE WIND ENERGY 975 Wenlong Ming M17 received the B Eng and M Eng degrees in Automation from Shandong University Jinan China in 2007 and 2010 respec tively and the PhD degree in Automatic Control and Systems Engineering from the University of Sheffield Sheffield UK in 2015 He has been a Lecturer of Power Electronics with Cardiff University Cardiff U K since 2016 and a Senior Research Fellow funded by Compound Semiconductor Applications Catapult UK for 5 years since 2020 His current research interests include mediumvoltage dc systems for electricity distribution networks and characterization modeling and applications of widebandgap compound semiconductors Dr Ming was the winner of the prestigious IET Control Automation Doctoral Dissertation Prize in 2017 Jianzhong Wu M14 received the BS MS and PhD degrees in electrical engineering from Tianjin University Tianjin China in 1999 2002 and 2004 respectively He is currently a Professor of Multivector Energy Systems and the Head of the School of Engineering Cardiff University Cardiff UK His current research interests include energy infrastructure and smart grids Prof Wu is an Associate Editor for Applied Energy He is a CoDirector of UK Energy Research Center and EPSRC Supergen Hub on Energy Net works Wuhua Li M09 received the BSc and PhD degrees in Power Electronics and Electrical Engi neering from Zhejiang University Hangzhou China in 2002 and 2008 respectively From 2004 to 2005 he was a Research Intern and from 2007 to 2008 a Research Assistant in the GE Global Research Center Shanghai China From 2008 to 2010 he joined the College of Electrical Engineering Zhejiang University as a Post doctor In 2010 he was promoted to an Associate Professor Since 2013 he has been a Full Professor at Zhejiang University From 2010 to 2011 he was a Ryerson University Postdoctoral Fellow with the Department of Electrical and Computer Engineering Ryerson University Toronto ON Canada He is currently the Executive Deputy Director of the National Specialty Laboratory for Power Electronics and the Vice Director of the Power Electronics Research Institute Zhejiang University His research interests include power devices converter topologies and advanced controls for high power energy conversion systems Dr Li has published more than 300 peerreviewed technical papers and holds over 50 issuedpending patents Due to his excellent teaching and research contributions Dr Li received the 2012 Delta Young Scholar from Delta Environmental Educational Founda tion 2012 Outstanding Young Scholar from National Science Foundation of China NSFC 2013 Chief Youth Scientist of National 973 Program 2019 Distinguished Young Scholar from National Science Foundation of China He serves as the Associate Editor of the Journal of Emerging and Selected Topics in Power Electronics IET Power Electronics CSEE Journal of Power and Energy Systems CPSS Transactions on Power Electronics and Applications Proceedings of the Chinese Society for Electrical Engineering Guest Editor of IET Renewable Power Generation for Special Issue DC and HVDC system technologies Member of Editorial Board for Journal of Modern Power System and Clean Energy He received one National Natural Science Award and four Scientific and Technological Achievement Awards from Zhejiang Provincial Government and the State Educational Ministry of China He was appointed as one of the Most Cited Chinese Researchers by Elsevier since 2014 Xiangning He M95SM96F10 received the BSc and MSc degrees from Nanjing University of Aeronautical and Astronautical Nanjing China in 1982 and 1985 respectively and the PhD de gree from Zhejiang University Hangzhou China in 1989 From 1985 to 1986 he was an Assistant Engineer at the 608 Institute of Aeronautical Indus trial General Company Zhuzhou China From 1989 to 1991 he was a Lecturer at Zhejiang University In 1991 he obtained a Fellowship from the Royal Society of UK and conducted research in the Department of Computing and Electrical Engineering HeriotWatt University Edinburgh UK as a PostDoctoral Research Fellow for two years In 1994 he joined Zhejiang University as an Associate Professor Since 1996 he has been a Full Professor in the College of Electrical Engineering Zhejiang University He was the Director of the Power Electronics Research Institute the Head of the Department of Applied Electronics the Vice Dean of the College of Electrical Engineering and he is currently the Director of the National Specialty Laboratory for Power Electronics Zhejiang University His research interests are power electronics and their industrial applications Dr He is a Fellow of The Institute of Electrical and Electronics Engineers IEEE and was appointed as IEEE Distinguished Lecturer by the IEEE Power Electronics Society 20112015 He is also a Fellow of the Institution of Engineering and Technology formerly IEE UK Timothy C Green M89SM02F19 received a BSc Eng first class honors from the Imperial College London UK in 1986 and a PhD from HeriotWatt University Edinburgh UK in 1990 He is a Professor of Electrical Power Engineering at Imperial College London and Director of the Energy Futures Lab with a role of fostering interdisciplinary energy research across the university His research is focused on using the flexibility of power electronics to further the decarbonization of electricity systems by easing the integrations of renewable sources and EV charging In HVDC he has contributed converter designs that strike improved tradeoffs between power losses physical size and fault handling In distribution systems he has pioneered the use of soft open points and the study of stability of grid connected inverters Prof Green is a Chartered Engineer in the UK and a Fellow of the Royal Academy of Engineering