Study on Reactive Power Compensation Strategies for Long Distance Submarine Cables Considering Electrothermal Coordination

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Journal of Marine Science and Engineering

Article Study on Reactive Power Compensation Strategies for Long Distance Submarine Cables Considering Electrothermal Coordination

Gang Liu 1 , Mingming Fan 1, Pengyu Wang 1,* and Ming Zheng 2

1 School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China; [email protected] (G.L.); [email protected] (M.F.) 2 China Energy Engineering Group Guangdong Electric Power Design Institute Co., Ltd., Guangzhou 510663, China; [email protected] * Correspondence: [email protected]; Tel.: +86-150-1198-8556

Abstract: Long-distance high voltage alternating current (AC) submarine cables are widely used to connect offshore wind farms and land power grids. However, the transmission capacity of the submarine cable is limited by the capacitive charging current. This paper analyzes the impacts of reactive power compensation in different positions on the current distribution on long-distance submarine cable transmission lines, and tests the rationality of the existing reactive power compensation schemes based on electrothermal coordination (ETC). Research shows that compensation at the sending end has obvious impacts on current distribution along the cable, and the maximum current occurs at the sending or receiving end. Moreover, the reactive power compensation at sending end will reduce the current at receiving end of the line. On the contrary, it will increase the current at sending end. Compared with the directly buried laying method of the submarine cable in the landing section, the cable trench laying method can increase the cable ampacity of the landing section and reduce the reactive power compensation capacity at the sending end. The ampacity is the current Citation: Liu, G.; Fan, M.; Wang, P.; representation of the thermal limits of the cable. ETC exploits the cable ampacity to coordinate Zheng, M. Study on Reactive Power current distribution on transmission lines under existing reactive power compensation schemes, Compensation Strategies for Long thus optimizing the reactive power compensation schemes and avoiding the bottleneck point of Distance Submarine Cables cable ampacity. Considering Electrothermal Coordination. J. Mar. Sci. Eng. 2021, 9, Keywords: submarine cables; charging current; reactive power compensation; cable ampacity; 90. https://doi.org/10.3390/ electrothermal coordination jmse9010090

Received: 17 December 2020 Accepted: 12 January 2021 1. Introduction Published: 15 January 2021 Wind energy, as an efﬁcient clean energy, has been increasingly valued. The utilization

Publisher’s Note: MDPI stays neutral of wind energy to generate electricity can enrich energy supply systems and reduce envi- with regard to jurisdictional claims in ronment pollution. In Europe, there were 3412 MW of installed capacity being increased, published maps and institutional afﬁl- and about 500 wind turbines were installed in 2019, making Europe the world leader in iations. the development of offshore wind power [1]. Compared with Europe, the wind power has been developing rapidly in China in recent years. The wind power generation in 2019 was 405.7 billion kW·h, accounting for 5.5% of total power generation [2]. Compared with the onshore wind power generation, the offshore wind power is rich in resources and has great development potential. The advantages of wind power in offshore wind farms, such as Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. high wind speed, being more stable, and having less impact on the environment, etc., are This article is an open access article attracting attention from more and more countries. distributed under the terms and High-voltage AC cable and high-voltage direct current (DC) cable are commonly conditions of the Creative Commons used in offshore wind power transmission lines. High voltage AC transmission has the Attribution (CC BY) license (https:// advantages of simple structure and low cost. When the transmission distance is long, creativecommons.org/licenses/by/ the transmission capacity of high-voltage AC cables is greatly affected by the charging 4.0/). current, and the loss caused by reactive power exchange will be more obvious [3,4]. The

J. Mar. Sci. Eng. 2021, 9, 90. https://doi.org/10.3390/jmse9010090 https://www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2021, 9, 90 2 of 17

transmission capacity of high-voltage DC cable is large, and the loss is low. However, the construction and operation costs are high, requiring building offshore and onshore converter stations [5]. These disadvantages have motivated some researches to look for methods to extend the feasibility of the high-voltage AC cable alternative. Aiming at the losses problem caused by the transmission system of high-voltage AC submarine cables in offshore wind farms, there are two common methods. One is to change the mode of system operation: To use lower operating frequency or to change the transmission voltage to reduce losses. In 2017, Gustavsen and Mo [6] proposed to improve the transmission capacity of the submarine cables by continuously changing the operating voltage of the long-distance submarine cables according to the output power of the wind farm. Using a lower frequency (less than the standard 50/60 Hz) to reduce the charging current on the transmission line and the skin effect on the conductor surface was analyzed in Ref. [7]. Another alternative is to consider using external equipment to compensate reactive power to reduce reactive current. The reactive power compensation plans for submarine cable transmission lines mainly include the single-terminal compensation, the two-terminal compensation, and the middle line compensation, also the conﬁguration scheme considering the comprehensive utilization of the reactive power output capacity of wind turbines. The middle line compensation of submarine cable transmission lines was considered by Gatta in 2011 [8]. Abram and Ola [9] designed the reactive power allocation plan of offshore wind farm transmission systems based on the reactive power capacity of wind turbines themselves and the high resistance of power grid side. In general, regarding the requirements of reactive power exchange and reactive power compensation strategies, different rules have been set in some European countries, Denmark, Germany, and Britain, which rule power factors of interconnection point within a certain range [10–12]. These rules are more considered from the point of view of transmission system operation, but the impacts of reactive power compensation strategies on current on the transmission line is seldom considered. Under the condition of satisfying the steady operation of the system, the thermal limits of long-distance submarine cables are also an important problem. The output submarine cables of offshore wind farms will pass through different laying sections, relating to various laying environments. Therefore, the steady-state ampacity of each laying section may vary greatly [13]. The current research is mainly focused on considering more environmental factors and establishing more accurate models to calculate the cable ampacity of submarine cables [14–18]. However, long-distance submarine cables are also affected by charging current. The reactive power compensation can improve the transmission power factors and it also changes the current distribution on the submarine cable transmission line [19]. For some laying sections with poor heat dissipation condition, when the wind farm is fully loaded or overloaded, some submarine cable sections may overheat to accelerate the aging of submarine cable insulation [20,21]. In this paper, an accurate PI equivalent model is used to calculate the current distribution in the long-distance submarine cable transmission line. Based on this model, impacts of various reactive power compensation schemes on the current distribution in the transmission line is analyzed and simulated. Then, the ampacity of the long-distance submarine cable is calculated under different laying methods based on IEC60287 standard [22]. Research tested the rationality of the existing reactive power compensation schemes from the point of view of electrothermal coordination (ETC) [23,24]. Cable ampacity is the current representation of the cable thermal limits. The ETC approach for system operation is compatible with and can determine more reasonable reactive power compensation schemes. It can avoid the occurrence of ampacity bottlenecks and provide a reference for the reactive power compensation schemes of the offshore wind farm output cables.

2. Electrical Calculation Model of HVAC Cables in Offshore Wind Farm 2.1. Structure of Offshore Wind Power System The offshore wind power generation system based on high-voltage AC transmission is shown in Figure1. It mainly consists of three parts: The ﬁrst one is the offshore wind J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 3 of 18

2. Electrical Calculation Model of HVAC Cables in Offshore Wind Farm J. Mar. Sci. Eng. 2021, 9, 90 3 of 17 2.1. Structure of Offshore Wind Power System The offshore wind power generation system based on high-voltage AC transmission is shown in Figure 1. It mainly consists of three parts: The first one is the offshore wind turbineturbine generator, generator, and and its function its function is to isuse to the use rotation the rotation of wind of turbine winds turbines to gener toate generateelec- tricity.electricity. The second The second part is part the istransformation the transformation part. The part. generated The generated electric energy electric is energy con- is centratedconcentrated through through the array the array cables, cables, and andthen thenthe voltage the voltage is raised is raised by the by offshore the offshore booster booster station.station. The The third third part part is isthe the transmission transmission part, part, where where the the electric electricityity raised raised by the by theoffshore offshore boosterbooster station station is isfinally ﬁnally transmitted transmitted to tothe the onshore onshore terminal terminal of the of thelanding landing point point through through thethe long long-distance-distance submarine submarine cables. cables. As As the the offshore offshore wind wind farms farms are aregenerally generally built built in the in the oceanocean areas areas far far from from the the coast, coast, the charging powerpower perper unitunit lengthlength ofof submarine submarine cable cable is is very verylarge, large, which which will will cause cause a large a large charging charging current current on on the the submarine submarine cables cables andand restrictrestrict the thetransmission transmission capacity capacity of of the the whole whole wind wind farm farm system system [ 25[25].]. According According toto literatureliterature [[26],26], the thewind wind farms farms should should meet meet the the requirements requirements of beingof being able able toarrange to arrange the the active active power power output outputand the and reactive the reactive power power output. output. Therefore, Therefore, for offshore for offshore wind wind farms, farms, the reactivethe reactive power powercompensation compensation is carried is carried out at out the at offshore the offshore booster booster stations stations and and the onshorethe onshore centralized cen- tralizedcontrol control center basedcenter onbase thed on principles the principles of section of section dividing dividing and local and balancelocal balance of reactive of reactivepower compensation,power compensation, and reactive and reactive power power compensation compensation equipment equipment such such as reactor, as reac- SVC, tor,or STATCOMSVC, or STATCOM are usually are installedusually installed [10,27]. [10,27].

FigureFigure 1. 1.ModelModel diagram diagram of ofan an offshore offshore wind wind farm farm connected connected to a to power a power grid grid..

2.2.2.2. Cable Cable D Designesign and and Characteristics Characteristics TheThe structure structure of of high high-voltage-voltage submarine submarine cable cable can can be bedivided divided into into the thesingle single-core-core and and thethe three three-core.-core. Compared Compared with with the the single single-core-core structure, structure, the the three three-core-core submarine submarine cabl cablee hashas less less loss loss and and low laying cost.cost. WithWith thethe maturity maturity of of manufacturing manufacturing technology, technology, the the three- threecore-core high-voltage high-voltage submarine submarine cable cable has has been been applied applied increasingly increasingly to the to trans-seathe trans-sea power J. Mar. Sci. Eng. 2021, 9, x FOR PEERpowertransmission REVIEW transmission [28]. A[28]. simpliﬁed A simplified cross cross section section drawing drawing of a of typical a typical three-core three-co submarinere sub-4 of 18

marinecable iscable shown is shown in the in Figure the Figure2. 2.

FigureFigure 2.2. SimplifiedSimplified cross section section of of three three-core-core submarine submarine cable cable.. 1– 1–corecore conductor; conductor; 2– cross 2–cross-linked-linked polyethenepolyethene (XLPE)(XLPE) insulationinsulation layer;layer; 3–swelling3–swelling tape; 4–metal4–metal sheath; 5 5–PE–PE sheath; 6 6–filling–filling layer and and wrapping tape; 7–inner sheath; 8–armor layer; 9–outer serving; 10–fiber layer [28]. wrapping tape; 7–inner sheath; 8–armor layer; 9–outer serving; 10–fiber layer [28]. The high-voltage AC submarine cable consists of three cores and outer material. The wire core materials from inside to outside successively are water-blocking copper conductor stranded by copper wires, conductor screen, cross-linked polyethene (XLPE) insulating layer, insulating screen, swelling tape, lead alloy sheath, anti-corrosion sheath, and filling layer. The outer materials from inside to outside successively are bedding, armor layer, and outer serving. In the filling layer, fiber optic units are usually distributed as channels for wind farm communication and submarine cable monitoring signal. The main structure parameters of the 220 kV, 3 × 500 mm2 three-core submarine cable are shown in Table 1.

Table 1. Structural parameters of submarine cables.

Layer Structure Thickness/mm Outer Radius of Structure/mm Number 1 Core conductor − 13.3 2 XLPE insulation 27.0 43.7 3 Swelling tape 0.5 44.7 4 Metal sheath 3.5 48.2 5 PE sheath 3.3 51.5 6 Filling layer 0.6 112.15 7 Inner sheath 1 113.65 8 Armored layer 6.0 119.65 9 Outer serving 4.0 123.65

2.3. Lumped Parameter Model of Submarine Cables Due to the influence of charging current, problems such as overcurrent and overvoltage will occur on the long-distance submarine cables, which will affect the safe operation of lines. To calculate the value of current, voltage, and power on the submarine cable line, a suitable cable model should be selected. The accuracy and complexity of the model are two indexes that often need to be concerned. The models of submarine cables mainly include the PI-type equivalent model of lumped parameters and the Bergeron model and frequency-dependent model of distributed parameters; the Bergeron model ignores the series impedance and admittance of the cable line. The line is considered as a lossless line, and the overall loss of line is considered only at both ends of the line; the frequency-dependent model is applied for the transient overvoltage analysis and the harmonic analysis [19]. According to [19], in the field of steady-state analysis of power systems, choosing to

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The high-voltage AC submarine cable consists of three cores and outer material. The wire core materials from inside to outside successively are water-blocking copper conductor stranded by copper wires, conductor screen, cross-linked polyethene (XLPE) insulating layer, insulating screen, swelling tape, lead alloy sheath, anti-corrosion sheath, and filling layer. The outer materials from inside to outside successively are bedding, armor layer, and outer serving. In the filling layer, fiber optic units are usually distributed as channels for wind farm communication and submarine cable monitoring signal. The main structure parameters of the 220 kV, 3 × 500 mm2 three-core submarine cable are shown in Table1.

Table 1. Structural parameters of submarine cables.

2.3. Lumped Parameter Model of Submarine Cables Due to the inﬂuence of charging current, problems such as overcurrent and overvoltage will occur on the long-distance submarine cables, which will affect the safe operation of lines. To calculate the value of current, voltage, and power on the submarine cable line, a suitable cable model should be selected. The accuracy and complexity of the model are two indexes that often need to be concerned. The models of submarine cables mainly include the PI-type equivalent model of lumped parameters and the Bergeron model and J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEWfrequency-dependent model of distributed parameters; the Bergeron model ignores5 the of 18 series impedance and admittance of the cable line. The line is considered as a lossless line, and the overall loss of line is considered only at both ends of the line; the frequency-dependent model is applied for the transient overvoltage analysis and the harmonic analysis [19]. use complex cable models cannot improve the accuracy of the problems analyzed. There- According to [19], in the ﬁeld of steady-state analysis of power systems, choosing to use fore, the accurate PI equivalent circuit model is considered in this paper, as shown in Fig- complex cable models cannot improve the accuracy of the problems analyzed. Therefore, ure 3. the accurate PI equivalent circuit model is considered in this paper, as shown in Figure3.

FigureFigure 3. 3.PIPI equivalent equivalent model model of of transmission transmission lines lines..

WhereWhere,, RR isis the the resistance resistance of of the the circuit, circuit, Ω;Ω L; Lis is the the inductance inductance of of the the circuit, circuit, H; H; GG isis thethe conduct conductanceance of of the the circuit, circuit, S; S; CC isis capacitance, capacitance, F. F. The The above above parameters parameters are are calculated calculated byby Carson Carson–Clem–Clem formula formula [29], [29], as as shown shown in in Table Table 2.2. The The impedance impedance and and admittance admittance of of the the submarinesubmarine cable cable PI PI equivalent equivalent circuit circuit are are respectively respectively represented represented by by ZZ andand Y.Y. Z(ω)= R + jωL (1) Z  =R+j  L (1) Y(ω)= G/2 + jωC/2 (2) Y  =G/2+j  C/2 (2)

Table 2. Distribution parameters of three-core AC submarine cable.

Resistance Inductance Conductance Capacitance Parameters Ω/km mH/km S/km µF/km Value 0.0488 0.43 2.1110−8 0.1283

According to literature [30], the relationship between voltage and current at the sending and receiving ends of the line is shown as follows:

coshl Z Y sinh  l Z sinh  l     c2   c    Vs1    Vr1     1    (3) I ZYYsinh lYY  (  )cosh  l cosh  lZY  sinh  l  I s1  c1 2    1 2    c 1    r1  Zc  

where Y1 and Y2 represent equivalent susceptance of inductors installed at the sending and receiving ends of HVAC cable for compensation; Vs1, Vr1 and Is1, Ir1, respectively represent the voltage and current at sending and receiving ends of line; l is the length of the line; γ is the transmission coefficient of line; and Zc is the characteristic impedance of the line.

Z  Zc   (4) Y 

   ZY    (5)

In order to accurately calculate the current and voltage at each point along the line, in literature [6], the transmission line of long-distance submarine cable is evenly divided into N segments of PI equivalent circuits, then the length of each section is Lseg = L/N, as shown in Figure 4. In Figure 4, V1, V2...Vn+1 and I1, I2...In+1 are respectively representing the voltage and current value of each PI equivalent circuit connection node from the sending end to the receiving end.

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Table 2. Distribution parameters of three-core AC submarine cable.

Resistance Inductance Conductance Capacitance Parameters Ω/km mH/km S/km µF/km Value 0.0488 0.43 2.11 × 10−8 0.1283

According to literature [30], the relationship between voltage and current at the sending and receiving ends of the line is shown as follows:

. . " # " cosh(γl) + Z Y sinh(γl) Z sinh(γl) #" # Vs1 c 2 c Vr1 . = . (3) 1 + Z Y Y sinh(γl) + (Y + Y ) cosh(γl) cosh(γl) + Z Y sinh(γl) Is1 Zc c 1 2 1 2 c 1 Ir1

where Y1 and Y2 represent equivalent susceptance of inductors installed at the sending and receiving ends of HVAC cable for compensation; Vs1, Vr1 and Is1, Ir1, respectively represent the voltage and current at sending and receiving ends of line; l is the length of the line; γ is the transmission coefﬁcient of line; and Zc is the characteristic impedance of the line. s Z(ω) Z (ω) = (4) c Y(ω)

q γ(ω) = Z(ω)Y(ω) (5)

In order to accurately calculate the current and voltage at each point along the line, in literature [6], the transmission line of long-distance submarine cable is evenly divided into N segments of PI equivalent circuits, then the length of each section is L = L/N, as shown J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW seg 6 of 18 J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEWin Figure 4. In Figure4, V1, V2...Vn+1 and I1,I2...In+1 are respectively representing the 6 of 18 voltage and current value of each PI equivalent circuit connection node from the sending end to the receiving end.

V1 V2 Vn+1 Sending V1 V2 Receiving Vn+1 end Sending1 2 n end Receiving I1 end I2 1 2 In+1 n end I1 I2 In+1 Figure 4. Segmentation of submarine cable into n sections for assessment of internal currents and voltages. FigureFigure 4. 4. SegmentationSegmentation of submarine cable cable into into n n sections sections for for assessment assessment of internal of internal currents currents and voltages.and voltages. According to literature [31], in this paper, each section is considered as 1 km. For a According to literature [31], in this paper, each section is considered as 1 km. For a submarine cablesubmarine withAccording L km cable length, withto literatureitL willkm be length, divided [31], it willin into this be dividedL paper, sections into each ofL PIsections section equivalent of is PI considered equivalent circuit. circuit. as 1 km. For a The node analysissubmarineThe method node analysis cableis used with method to calculate L km is used length, the to calculatevoltage it will beand the divided voltage current andinto value current L sections on each value ofnode on PI each equivalent node circuit. in MATLAB, asThe inshown MATLAB, node in analysis Figure as shown 5. method in Figure is used5. to calculate the voltage and current value on each node in MATLAB, as shown in Figure 5.

Figure 5. Figure 5. Submarine cableSubmarine lines with cable n sections lines with of n PI sections equivalent of PI equivalent circuits. circuits.

In Figure Figure5, Vs a nd5. Submarine Vr are the cable voltage lines values with n at sections sending of PIand equivalent receiving ci endsrcuits .respectively; IS and Ir are respectively the input and output current values at sending and receiv- r ing ends; QS, Qr, andIn Q Figurem are for 5, theVs reactiveand V arecompensation the voltage power values capacity at sending at the and sending receiving ends respec- end, receiving end,tively; and IS middleand Ir are line, respectively respectively. the According input and to output Figure current5, the mathematical values at sending and receiv- model in MATLABing ends; for solving QS, Q rthe, and line Q currentm are for distribution the reactive is showncompensation as below. power In this capacity part, at the sending taking the reactiveend, receivingpower compensation end, and middle at 1/2 line, of long respectively.-distance submarine According cables to Figure as an 5, the mathematical example to showmodel the mathematic in MATLAB model for solving. the line current distribution is shown as below. In this part, For sendingtaking end: the reactive power compensation at 1/2 of long-distance submarine cables as an example to show the mathematic model.

For sending end: IPVs= / 3 1 cos 1     2 I0= V 1 / i * V 1 / Qs   IPV= / 3 cos    s 1 1  III1= s 0   I= V  / i * V2 / Q (6) IVY   0 1 1 s   y1 1         III1= s 0 IIIz1 1  y 1    (6)     IVYy1 1  VVIZ2 1 z 1      IIIz1 1  y 1  For middle line: VVIZ      2 1z 1    VVIZn/ 2 1 n /2   For middle line: z n/2   IVYn/2 1   y n/2 1  VVIZ2      I= V  / i * Vn/ / 2 Q 1 n /2 z n/2  m n/ 2 1 n /2  1 m  (7)      IVY n/2 1  IIIIn/2 1z n/2  y ( n /2+1)y n/2  1 m      I= V  / i * V2 / Q IIIz n/2 1 = n/ 2 1   y n /m 2  1 n/ 2 1 n /2  1 m  (7)       IIIIn/2 1z n/2  y ( n /2+1)  m For receiving end:     IIIz n/2 1 = n/ 2 1  y n / 2  1 

For receiving end:

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In Figure5, Vs and Vr are the voltage values at sending and receiving ends respectively; IS and Ir are respectively the input and output current values at sending and receiving ends; QS, Qr, and Qm are for the reactive compensation power capacity at the sending end, receiving end, and middle line, respectively. According to Figure5, the mathematical model in MATLAB for solving the line current distribution is shown as below. In this part, taking the reactive power compensation at 1/2 of long-distance submarine cables as an example to show the mathematic model. For sending end:  Is = P/(3V1 ∗ cos ϕ1)  . .  = ∗ 2  I0 V1/ i V1 /Qs  . . .  I1 = Is − I0 . . (6) Iy1 = V1 ∗ Y  . . .   Iz1 = I1 − Iy1  . . .  V2 = V1 − Iz1 ∗ Z For middle line:  . . . Vn/2+1 = Vn/2 − Iz(n/2) ∗ Z  . .   Iy(n/2+1) = Vn/2+1 ∗ Y  . . 2 Im = V + / i ∗ V + /Qm (7) . n/2. 1 .n/2 1 .   In/2+1 = Iz(n/2) − Iy(n/2+1) − Im  . . .  Iz(n/2+1) = In/2+1 − Iy(n/2+1) For receiving end:  . . . Vn+1 = Vn − Izn ∗ Z  . .   Iy(n+1) = Vn+1 ∗ Y  . . 2 I = Vn+1/ i ∗ Vn+1 /Qr (8) . d . .   In+1 = Izn − Iy(n+1)  . . .  Ir = In+1 − Id

where P is the active power transmitted by the submarine cable line, I0, Im, and Id is the current of reactive power compensation equipment on the sending, middle line, and receiving end, respectively, Iy1 ... Iyn and Iz1 ... Izn are respectively representing the current of admittance and impedance of PI equivalent circuit, cosϕ1 is the transmission power factors of the sending end of the submarine cable line, and i is the unit of imaginary number.

3. Impacts of Reactive Power Compensation on Current Distribution of for Long-Distance Submarine Cables Due to the large capacitance of high-voltage submarine cables, plenty of reactive power will be generated. The reactive compensation is usually adopted to solve this problem. Because of the limitation of engineering conditions, the reactive compensation for the submarine cables cannot be conducted along the line, but can only be conducted centrally at both ends of the line or on the land halfway [27]. The inﬂuence of different reactive power compensation schemes on the current distribution of submarine cables is analyzed in detail below. Assuming that the rated voltage of long-distance submarine cable lines is 220 kV, the voltage at the sending end of the submarine cable transmission is 1.05 times of the rated voltage, as 232 kV, and the full load state will be the moment when the transmission power reaches 203.5 MW. As shown in Figure6, under no-load condition, the charging current distribution on the line has a linear relationship with the transmission distance. The farther the transmission distance is, the larger the current on the line will be. When the submarine cable line is half-loaded or fully loaded, the current at the receiving end of the line is much larger than that at the sending end of the line due to the large charging current of the cable without reactive compensation. For a 100 km submarine cable transmission line, the current at the line terminal reaches 220% and 138% of the current at sending end respectively under J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 7 of 18

   VVIZn1  n  zn     IVYy n1 n1      2 Id= V n1 / i * V n  1 / Q r  (8)     IIIn1 zn  y ( n +1)     IIIr= n 1  d 

where P is the active power transmitted by the submarine cable line, I0, Im, and Id is the current of reactive power compensation equipment on the sending, middle line, and receiving end, respectively, Iy1…Iyn and Iz1…Izn are respectively representing the current of admittance and impedance of PI equivalent circuit, cosφ1 is the transmission power factors of the sending end of the submarine cable line, and i is the unit of imaginary number.

3. Impacts of Reactive Power Compensation on Current Distribution of for Long-Dis- tance Submarine Cables Due to the large capacitance of high-voltage submarine cables, plenty of reactive power will be generated. The reactive compensation is usually adopted to solve this problem. Because of the limitation of engineering conditions, the reactive compensation for the submarine cables cannot be conducted along the line, but can only be conducted centrally at both ends of the line or on the land halfway [27]. The influence of different reactive power compensation schemes on the current distribution of submarine cables is analyzed in detail below. Assuming that the rated voltage of long-distance submarine cable lines is 220 kV, the voltage at the sending end of the submarine cable transmission is 1.05 times of the rated voltage, as 232 kV, and the full load state will be the moment when the transmission power reaches 203.5 MW. As shown in Figure 6, under no-load condition, the charging current distribution on the line has a linear relationship with the transmission distance. The farther the transmission distance is, the larger the current on the line will be. When the submarine cable line is half-loaded or fully loaded, the current at the receiving end of the line is much larger than that at the sending end of the line due to the large charging current of the cable without reactive compensation. For a 100 km submarine cable transmission line, the current at the line terminal reaches 220% and 138% of the current at sending end re- J. Mar. Sci. Eng. 2021, 9, 90 spectively under half-load and full load conditions. For some laying7 of 17sections with poor heat dissipation conditions, the current on the submarine cable line may exceed its am-

pacityhalf-load when and the full load load is conditions. high, causing For some the laying cable sections overheated with poor operation, heat dissipation which will accelerate the conditions,aging of thethe current cable on insulation the submarine and cable reduce line may the exceed service its ampacity life of when the thecable. load is high, causing the cable overheated operation, which will accelerate the aging of the cable insulation and reduce the service life of the cable.

800 Full load 700 Half load No load 600

500

J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW400 8 of 18

Current(A) 300

200

In100 order to analyze the influence of the different shunt compensation locations on the

line current,0 the reactive compensations are conducted respectively to the sending end 0 20 40 60 80 100 and receiving end of Cablea certain length (km) length submarine cable line. As shown in Figures 7 and 8, the current and voltage distribution curves of the submarine cable with different reactive Figure 6. Current distribution of submarine cables under different load conditions without reactive power compensations at the sending end are obtained. According to Figure 7, the current Figurepower 6. compensation.Current distribution of submarine cables under different load conditions without reac- at the sending end of the submarine cable line is related to the amount of reactive com- tive power compensation. pensation.In order The to larger analyze the the reactive inﬂuence power of the different compensation shunt compensation at the sending locations end, on the the larger the currentline current, at the thesending reactive end. compensations This is beca areuse conducted the square respectively of the to current the sending at endthe andsending end is receiving end of a certain length submarine cable line. As shown in Figures7 and8 , the equalcurrent to the and sum voltage of distribution the squares curves of ofthe the active submarine current cable withand different reactive reactive current. power The relation betweencompensations the current at the at sending the sending end are obtained.end of submarine According tocable Figure line7, the and current the reactive at the compen- sationsending is as end follows: of the submarine cable line is related to the amount of reactive compensation. The larger the reactive power compensation at the sending end, the larger the current at the sending end. This is because the square of the current2 at the sending2 end is equal to the sum of the squares of the active current andP reactive  current.Qs  The relation between I1      (9) the current at the sending end of submarine cable line and the reactive compensation is 3VVs cos   3 s  as follows: s 2 2 P Qs where P is the active powerI transmitted= by the+ submarine cable line, W; QS (9)is the reactive 1 3V cos θ 3V power compensated at the sending ends of the line,s Var. where P is the active power transmitted by the submarine cable line, W; QS is the reactive power compensated at the sending end of the line, Var.

680 40 MVar 60 MVar 660 80 MVar 100 MVar 640

620

600 Current (A) Current 580

560

540

520 0 20 40 60 80 100 Cable length (km)

Figure 7. Current distribution of submarine cables under full load with different reactive power Figurecompensation 7. Current at thedistribution sending end. of submarine cables under full load with different reactive power compensation at the sending end.

135

134

133

132

131

Voltage (kV) Voltage 130

129 0 MVar 50 MVar 128 120 MVar 180 MVar 127 0 20 40 60 80 100 Cable length (km)

Figure 8. Voltage distribution of submarine cables under full load with different reactive power compensation at the sending end.

On the other hand, the more reactive power compensated at sending end, the smaller the current at the receiving end is. This is because the inductive current of reactive power

J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 8 of 18

In order to analyze the influence of the different shunt compensation locations on the line current, the reactive compensations are conducted respectively to the sending end and receiving end of a certain length submarine cable line. As shown in Figures 7 and 8, the current and voltage distribution curves of the submarine cable with different reactive power compensations at the sending end are obtained. According to Figure 7, the current at the sending end of the submarine cable line is related to the amount of reactive compensation. The larger the reactive power compensation at the sending end, the larger the current at the sending end. This is because the square of the current at the sending end is equal to the sum of the squares of the active current and reactive current. The relation between the current at the sending end of submarine cable line and the reactive compensation is as follows:

2 2 P  Qs  I1      (9) 3VVs cos   3 s 

where P is the active power transmitted by the submarine cable line, W; QS is the reactive power compensated at the sending end of the line, Var.

680 40 MVar 60 MVar 660 80 MVar 100 MVar 640

620

600 Current (A) Current 580

560

540

520 0 20 40 60 80 100 Cable length (km)

Figure 7. Current distribution of submarine cables under full load with different reactive power

J. Mar. Sci. Eng. 2021, 9, 90 compensation at the sending end. 8 of 17

135

134

133

132

131

Voltage (kV) Voltage 130

129 0 MVar 50 MVar 128 120 MVar 180 MVar 127 0 20 40 60 80 100 Cable length (km)

Figure 8. Voltage distribution of submarine cables under full load with different reactive power Figurecompensation 8. Voltage at thedistribution sending end. of submarine cables under full load with different reactive power compensation at the sending end. On the other hand, the more reactive power compensated at sending end, the smaller the current at the receiving end is. This is because the inductive current of reactive power compensationOn the other at thehand, sending the endmore compensates reactive power part of thecompensated capacitive current at sending of the line, end, the smaller the makingcurrent the at reactive the receiving current of end the line is. decrease. This is Accordingbecause the to the inductive U-shape current current curve of in reactive power Figure7, in the case of sending end compensation, the maximum current of the whole line appears at the sending end or receiving end. In Figure8, in the case of no compensation, the voltage on the line presents a downward trend, but applying reactive compensation at the sending end of the line will increase the voltage value on the line. When the reactive compensation reaches a certain degree, the voltage at the receiving end will exceed the voltage value at the sending end of the line. Applying a certain amount of reactive compensation to raise the voltage at the receiving end of the line can prevent the low voltage of the junction point and improve the stability of the system. The reactive power compensation for the receiving end does not change the current distribution of the line. According to the literature [30], the compensation for the receiving end can improve the power factor of the junction point. Middle line compensation refers to reactive power compensation on the submarine cable transmission line between the sending and receiving end. Compared with the compensation at the sending and receiving end, the reactive power compensation equipment are installed in the offshore booster station and the onshore centralized control center, respectively. Because submarine cables usually cross the sea, there are higher technical and economic requirements for the compensation at the middle line. For some submarine cable transmission lines crossing the island, the reactive power compensation can be considered in the island section. As shown in Figure9, only the middle line of the submarine cable transmission line is compensated, and the current distribution from the sending end to the middle line does not change, while the reactive power compensation in the middle line will greatly reduce the current distribution from the middle section to receiving end. The current distribution results along the line after reactive power compensation at 1/3,1/2 and 2/3 of the long-distance submarine cable are calculated respectively, as shown in Figure 10. According to the Figure 10, the results show that the middle line compensation with the same capacity in different positions can reduce the current of the compensation point. But it will not change the current distribution trend from the compensation point to the receiving end. J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 9 of 18

compensation at the sending end compensates part of the capacitive current of the line, making the reactive current of the line decrease. According to the U-shape current curve in Figure 7, in the case of sending end compensation, the maximum current of the whole line appears at the sending end or receiving end. In Figure 8, in the case of no compensation, the voltage on the line presents a downward trend, but applying reactive compensation at the sending end of the line will increase the voltage value on the line. When the reactive compensation reaches a certain degree, the voltage at the receiving end will exceed the voltage value at the sending end of the line. Applying a certain amount of reactive compensation to raise the voltage at the receiving end of the line can prevent the low voltage of the junction point and improve the stability of the system. The reactive power compensation for the receiving end does not change the current distribution of the line. According to the literature [30], the compensation for the receiving end can improve the power factor of the junction point. Middle line compensation refers to reactive power compensation on the submarine cable transmission line between the sending and receiving end. Compared with the compensation at the sending and receiving end, the reactive power compensation equipment are installed in the offshore booster station and the onshore centralized control center, respectively. Because submarine cables usually cross the sea, there are higher technical and economic requirements for the compensation at the middle line. For some submarine cable transmission lines crossing the island, the reactive power compensation can be considered in the island section. As shown in Figure 9, only the middle line of the submarine cable transmission line is compensated, and the current distribution from the sending end to the middle line does not change, while the reactive power compensation in the middle line will greatly reduce the current distribution from the middle section to receiving end. The current distribution results along the line after reactive power compensation at 1/3,1/2 and 2/3 of the long-distance submarine cable are calculated respectively, as shown in Fig- ure 10. According to the Figure 10, the results show that the middle line compensation with the same capacity in different positions can reduce the current of the compensation point. But it will not change the current distribution trend from the compensation point

J. Mar. Sci. Eng. 2021, 9, 90 to the receiving end. 9 of 17

0 MVar 750 30 MVar 60 MVar 90 MVar 700

650 Current (A) 600

550

500 J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 0 20 40 60 80 100 10 of 18

Cable length (km)

Figure 9. Current distribution of submarine cables under full load with different reactive power Figurecompensation 9. Current at the distribution middle line. of submarine cables under full load with different reactive power compensation at the middle line. 1/3 750 1/2 2/3

700

650 Current(A) 600

550

500 0 20 40 60 80 100 Cable length (km) Figure 10. Current distribution of long-distance submarine cables under reactive power compensa- Figuretion at10. different Current positions. distribution of long-distance submarine cables under reactive power compensation at different positions. To sum up, the receiving end compensation for submarine cable transmission lines will not change the current distribution on the lines, but it can be used as one of the measures to improveTo sum the up, power the factor receiving of junction end points. compensation The compensation for forsubmarine the mid-line cable can reduce transmission lines willthe not current change distribution the current from the distribution compensation point on the to the lines, receiving but end. it can However, be used the as one of the measuresmiddle sectionto improve of the submarinethe power cable factor line isof usually junction sea area,points. the costThe for compensation construction for the mid- and maintenance of reactive compensation equipment for the mid-line is high. Therefore, lineto can reduce reduce the reactive the current current distribution on the line and from increase the thecompensation transmission capacity point to of the the receiving end. However,line, the compensationthe middle forsection the sending of the end submarine of the line is cable usually line considered. is usually The reactivesea area, the cost for constructioncompensation and equipment maintena is installednce of in reactive offshore compensationbooster stations to equipment reduce investment for the mid-line is high.costs. Therefore, For the long-distance to reduce transmission the reactive lines current where sending on the end line compensation and increase cannot the be transmission satisﬁed, the mid-line compensation can be considered simultaneously. capacityThe of layingthe line, environment the compensation of submarine for cable the transmission sending end line of is the complex, line is and usually the considered. Theampacity reactive of compensation different laying sections equipment is different. is installed If the current in offshore in a section booster of the stations line to reduce investmentis greater thancosts. its For ampacity, the long the cable-distance core will transmission overheat, accelerating lines where the thermal sending aging end compensa- of the insulation, and reducing the service life of the cable. Therefore, it is necessary to tioncomprehensively cannot be satisfied, consider the the mid current-line distribution compensation in the submarine can be considered cable lines and simultaneously. the ampacityThe laying of each environment section, and select of thesubmarine appropriate cable submarine transmission cable laying line mode is andcomplex, and the ampacityreactive powerof different compensation laying scheme sections at the is initial different. stage of theIf the project current design, in it isa better section to of the line is greaterrealize than the economy its ampacity, of investment. the cable core will overheat, accelerating the thermal aging of the insulation, and reducing the service life of the cable. Therefore, it is necessary to com- prehensively consider the current distribution in the submarine cable lines and the ampacity of each section, and select the appropriate submarine cable laying mode and reactive power compensation scheme at the initial stage of the project design, it is better to realize the economy of investment.

4. Thermal Calculation Model of Submarine Cables For the long-distance transmission lines of high-voltage output submarine cables in offshore wind farms, the starting point is usually the offshore booster station. The offshore booster station collects the electric energy generated by the wind turbine and boosts it, and then connects to the power grid on land through the submarine cables. It is generally composed of two parts: The power transformation system and the offshore platform structure. Then, the laying environment of the submarine cables is constantly changing, which can be mainly divided into four sections: J-shape pipe section, seabed section, mud flat section, and landing section. Finally, the line reaches the terminal station on land, and output cable laying path for offshore wind farm is shown in Figure 11. Generally, the J- shape pipe section gets the submarine cable to enter the sea from the offshore booster platform and lead to the seabed through the protection pipe [14]. In the seabed section, the cable is usually buried in the ground, and the buried depth is usually between 2 and 3 m. The length of the mud flat section is generally short, and it is the transition section between the seabed section and the landing section, directly buried laying is usually adopted. The landing section is generally buried in soil or laid in cable trench, and the length of this section is between several hundred meters and one or two kilometers. In this paper, it is assumed that the length of the J-shape pipe section is 30 m, the length of

J. Mar. Sci. Eng. 2021, 9, 90 10 of 17

4. Thermal Calculation Model of Submarine Cables For the long-distance transmission lines of high-voltage output submarine cables in offshore wind farms, the starting point is usually the offshore booster station. The offshore booster station collects the electric energy generated by the wind turbine and boosts it, and then connects to the power grid on land through the submarine cables. It is generally composed of two parts: The power transformation system and the offshore platform structure. Then, the laying environment of the submarine cables is constantly changing, which can be mainly divided into four sections: J-shape pipe section, seabed section, mud flat section, and landing section. Finally, the line reaches the terminal station on land, and output cable laying path for offshore wind farm is shown in Figure 11. Generally, the J-shape pipe section gets the submarine cable to enter the sea from the offshore booster platform and lead to the seabed through the protection pipe [14]. In the seabed section, the cable is usually buried in the ground, and the buried depth is usually between 2 and 3 m. The length of the mud flat section is generally short, and it is the transition section between the seabed section and the landing section, directly buried laying is usually adopted. The J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 11 of 18 J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEWlanding section is generally buried in soil or laid in cable trench, and the length11 of 18 of this section is between several hundred meters and one or two kilometers. In this paper, it is assumed that the length of the J-shape pipe section is 30 m, the length of the mud flat sectionthe mud is flat 500 section m, the is length500 m, the of the length landing of thesection landing issection 2 km, is and 2 km, the and rest the of rest the of length the is the the mud flat section is 500 m, the length of the landing section is 2 km, and the rest of the seabedlength is section. the seabed section. length is the seabed section.

FigureFigure 11. Output cable cable laying laying path path for for offshore offshore wind wind farm farm.. 1—J 1—J-shape-shape pipe pipesection; section; 2–seabed 2–seabed section; Figure3–mudsection; 11. ﬂat3 –Outputmud section; flat cable section; 4–landing laying 4– lpathanding section; for section; offshore 5–offshore 5 –windoffshore farm booster booster. 1—J station- shapestation pipe platform; section; 6– 6–onshore o2nshore–seabed cen- centralized section;controltralized 3center. –controlmud flat center. section; 4–landing section; 5–offshore booster station platform; 6–onshore centralized control center. BasedBased on on the the structural structural parameters parameters of the ofthree the-core three-core submarine submarine cable, a thermal cable, pa- a thermal parameterrameterBased model on model the is establishedstructural is established parameters to calculate to calculate ofthe the ampacity three the-core of ampacity the submarine submarine of thecable, cable. submarine a The thermal thermal cable.pa- The rameterparameters model represent is established the heat to flow calculate through the ampacitythe materials of the of thesubmarine cable. A cable. steady The-state thermal ther- thermal parameters represent the heat ﬂow through the materials of the cable. A steady- parametersmal circuit representmodel of athe three heat-core flow submarine through the cable materials is as follows of the [ cable.32]: A steady-state ther- state thermal circuit model of a three-core submarine cable is as follows [32]: mal circuitIn Figure model 12, of θc ais three the conductor-core submarine temperature, cable isθ aas is followsthe environmental [32]: temperature of In Figure 12, θc is the conductor temperature, θa is the environmental temperature cable,In θFigure1 is the 12, metal θc is sheath the conductor temperature, temperature, θ2 is the armor θa is the layer environmental temperature, temperature Wc is the joule of of cable, θ is the metal sheath temperature, θ is the armor layer temperature, Wc is the cable,loss of θ 1conductor is the1 metal per sheath unit length, temperature, Wd is the θ2 dielectric is the armor2 loss layer of conductor temperature, insulation Wc is theper jouleunit W lossjoulelength, of lossconductor T1 ofis conductorthe thermalper unit per resistancelength, unit W length, dbetween is the dielectric dconductoris the dielectricloss and of conductor sheath, loss ofT2 insulation conductoris the thermal per insulation unitre- per length,unitsistance length, T 1of is thetheT 1lining thermalis the between thermal resistance sheath resistance between and armor, between conductor T3 is conductorthe and thermal sheath, and resistance T2 sheath, is the of thermal Tthe2 is outer the re- thermal sistanceresistancesheath ofof thethe of thecable,lining lining and between T between4 refers sheath to sheath the and thermal armor, and armor, resistance T3 is theT3 isthermalbetween the thermal resistance the cable resistance surfaceof the outer and of the outer sheathsheaththe surrounding of of the the cable, cable, medium. and and T4 Tλrefers41 isrefers the to ratio the to thethermal of the thermal metal resistance sheath resistance betweenloss to between the the conductor cable the surface cable loss, surface andand and thetheλ2 surroundingis surrounding the ratio of medium.the medium. armor λ layer1 λis1 theis loss theratio to ratio theof the conductor of metal the metal sheath loss. sheath loss to loss the toconductor the conductor loss, and loss, and λλ22 isis the the ratio ratio of ofthe the armor armor layer layer loss loss to the to conductor the conductor loss. loss. T1 T T1 1 c 1 2 a

T T2 T T T1 1 3 4 c 1 2 a

T1 T2 T3 T4 3Wc 1.5Wd 1.5Wd 1W c 2W c

3Wc 1.5Wd 1.5Wd 1W c 2W c

Figure 12. Steady-state thermal circuit model of three-core submarine cable. FigureFigure 12. 12. SteadySteady-state-state thermal thermal circuit circuit model model of three of three-core-core submarine submarine cable. cable. The heat flow generated by the core loss of the submarine cable changes with the load. From the above thermal circuit model and the relation of thermoelectric analogy The heat flow generated by the core loss of the submarine cable changes with the [32], according to the circuit node voltage method, the relation between temperature, heat load. From the above thermal circuit model and the relation of thermoelectric analogy flux, and thermal resistance of each part of the cable in steady state can be obtained: [32], according to the circuit node voltage method, the relation between temperature, heat flux, and thermal resistance of each part of the cableT in steady state can be obtained: 3WW 1.5  1    (10) c d3 c 1 T 3WW 1.5  1    (10) c d3 c 1 3WWWTc d 1 c  2   1   2 (11)

3WWWTc d 1 c  2   1   2 (11) 3WWWWTTc d 1 c   2 c 3  4   2   a (12)

3WWWWTTc d 1 c   2 c 3  4   2   a (12)

J. Mar. Sci. Eng. 2021, 9, 90 11 of 17

The heat ﬂow generated by the core loss of the submarine cable changes with the load. From the above thermal circuit model and the relation of thermoelectric analogy [32], according to the circuit node voltage method, the relation between temperature, heat ﬂux, and thermal resistance of each part of the cable in steady state can be obtained:

T (3W + 1.5W ) 1 = θ − θ (10) c d 3 c 1

3(Wc + Wd + λ1Wc)T2 = θ1 − θ2 (11)

3(Wc + Wd + λ1Wc + λ2Wc)(T3 + T4) = θ2 − θa (12) The allowable continuous ampacity of AC cable can be calculated according to the above equations and the empirical formula of ampacity calculation in IEC60287-1- 1 [22], namely:

h i 1  T1  2 θc − θa − Wd · 2 + n · (T2 + T3 + T4) I =   (13) R · T1 + n · R · (1 + λ1) · T2 + n · R · (1 + λ1 + λ2) · (T3 + T4)

where, I is the allowable continuous current of the cable, A; n is the core number of submarine cable conductor, and R is the AC resistance of conductor under operating temperature. The calculation of relevant parameters can be found in Ref. [22].

0 R = R 1 + Ys + Yp (14)

0 where, R is the DC resistance of conductor per unit length, Ω/m; Ys is the skin effect factor; and Yp is the adjacent effect factor.

0 00 λ1 = λ 1 + λ 1 (15)

0 The metal sheath loss includes circulation loss λ1 and eddy-current loss λ1”. The eddy-current loss is negligible for the three-core submarine cable. The calculation formula 0 for the circulation loss λ1 is as follows. R 1.5 0 = s λ 1 2 (16) R Rs 1 + ( X )

2s X = 2ω ∗ 10−7 ln (17) d

ρs Rs = [1 + αs(θ · η − 20)] (18) As where, S is the distance between conductor axes, m; d is the average diameter of the metal sheath, m; ρs is the conductivity of the metal sheath material, Ω·m; As is the cross-sectional 2 area of the metal sheath, mm ; αs is the resistance temperature coefﬁcient, 1/K; θ is the working temperature of conductor, ◦C; η is the ratio of the temperature of metal sheath to the temperature of conductor, were set as 0.7.

2 RA 2c 1 λ2 = 1.23 (19) 6 2 R dA 2.77RA10 ω + 1

where, RA is the AC resistance of armor layer at the highest temperature, Ω/m; c is the distance between the conductor axis and the center of submarine cable, m; dA is the average diameter of the armor layer, m. Wd = ωCU0 tan δ (20) J. Mar. Sci. Eng. 2021, 9, 90 12 of 17

where, C is the submarine cable capacitance per unit length, F/m; U0 is the voltage to the ground, V; tanδ is the insulation loss factor under power frequency and working temperatures, here taken as tanδ = 0.0005, w = 2πf. ρ T = K T G (21) 1 2π

where, ρT is the thermal resistance coefﬁcient of insulation, K·m/W; G is the geometric factor; and K is the shielding factor. ρ T = T G0 (22) 2 6π 0 where, G is the geometric factor; and ρT is the thermal resistance coefﬁcient between sheath and armor, K·m/W. 1 2t3 T3 = ρT ln 1 + 0 (23) 2π D a

where, ρT is the thermal resistance coefﬁcient of submarine cable outer sheath, K·m/W; 0 t3 is the thickness of outer sheath, m; Da is the outer diameter of the armor, m; and the calculation formula for the environmental thermal resistance T4 depends on the laying environment, as shown below:

 ρ  T In 4L  2π De  1 T4 = πD h(∆θ )0.25 (24)  e tr  U ρd Do 1  T4a + T4b + T4c = + + + π In D + 0.25 1 0.1(V Yθm)De 2 d πDoh(∆θ)

Equation (24) correspond to the calculation formulas of environmental thermal resistance under the laying methods of directly buried, cable trench, and J-shape pipe laying, respectively. Where, ρT is the thermal resistance coefficient of soil, K·m/W; L is the buried depth of submarine cables, m, which is the distance between the cable axis and the ground surface; De is the outside diameter of the cable, m; h is the coefficient of heat transfer 2 on the cable surface, W/m ·K; ∆θtr is the temperature rise when the air temperature in the cable trench is higher than the surrounding air temperature, K; T4a, T4b, and T4c are, respectively, the air thermal resistance, the J-shape pipe thermal resistance, and the pipe external thermal resistance, which are between the cable surface and the inner surface of the pipe; U, V, and Y are constants related to laying conditions; θm is the average temperature of medium between cables and pipelines, K; Do is the outer diameter of the pipe, m; Dd is the pipe inner diameter, m; ρd is the thermal resistance of J-shape pipe material, K·m/W; 2 hj is the coefficient of heat transfer on the surface of the J-shape pipe, W/m ·K; ∆θ is the temperature rise when the temperature of J-shape pipe is higher than the surrounding air temperature, K. For the four laying methods of output cables in offshore wind farms (J-shape pipe section, seabed section, mud flat section, and landing section), the parameter assumptions of different laying environments are given for the ampacity calculation, and the ampacity of different sections are calculated. The relevant parameters and calculation results are shown in Tables3 and4, respectively.

Table 3. Parameters of submarine cable laying conditions.

Material Parameters Value Thermal conductivity coefficient of soil at landing section (K·m/W) 1.2 Thermal conductivity coefficient of soil at mud flat section (K·m/W) 1 Thermal conductivity coefficient of soil at seabed section (K·m/W) 0.83 J-shape pipe inner diameter (mm) 468 J-shape pipe outer diameter (mm) 508 J. Mar. Sci. Eng. 2021, 9, 90 13 of 17

Table 4. Submarine cable laying conditions and ampacity.

Environment Laying Environment Laying Depth m Thermal Resistance T Ampacity A Temperature ◦C 4 J-shape pipe section 55 - 0.16 620 Seabed section 28.5 2.5 0.49 605 Mud ﬂat section 35 1 0.443 593 Landing section (directly buried) 35 1 0.532 557 Landing section (cable trench) 50 1 0.2766 582

5. Reactive Power Compensation Analysis of Submarine Cables Based on Electrothermal Coordination Due to the limitation of thermal stability, the submarine cable should meet the requirement that the current of the whole line should not be greater than its ampacity. Meanwhile, the operation principle of the high-voltage AC transmission system should also be considered. To maintain the stability of the system, the voltage excursion of sending and receiving end sections of the transmission line should be contained within a suitable range, and the power factors of offshore booster stations and onshore junction points also need to meet a certain range. The current distribution of long-distance submarine cable transmission line needs to meet the requirement of ampacity of each section under different laying modes. The relevant constraint conditions are shown as follows [10,30].

cos ϕ1 ≥ 0.95 (25)

cos ϕ2 = 1 (26)

0.97Vn ≤ Vs ≤ 1.07Vn (27)

0.97Vn ≤ Vr ≤ 1.07Vn (28)

Iline ≤ Irated (29)

where, cosϕ1 and cosϕ2 are the transmission power factors of the sending and receiving end of the submarine cable line, respectively; Vn is the rated voltage of the line at 220 kV; Iline is the current value in the submarine cable transmission line, A; Irated is the ampacity of each section of the line under different laying methods, A. For the long-distance submarine cable transmission lines, by considering the above constraints, the current distribution of different reactive power compensation schemes is analyzed. The more economical compensation schemes and landing section laying methods are selected, to realize the economic and safe operation of the submarine cable. The offshore wind farms transmit the maximum current at its full load. Being affected by charging current, the current of the line at full load may exceed its ampacity, so the full load condition is considered in the analysis below.

5.1. Directly Buried Laying Method of Landing Section First, the directly buried laying method is considered in the landing section. The ampacity of the directly buried laying method in the landing section, which is calculated from Table4, is 557 A. After calculation, for the submarine cable transmission lines with a length of 90 km or less, the ampacity will meet the requirement through conducting the reactive power compensation at sending end. The results calculated by MATLAB are shown in Figure 13. As shown in the ﬁgure above, the dotted line represents the ampacity of different laying sections of long-distance submarine cables. The bottleneck point of submarine cables ampacity occurs in the landing section. When there is no reactive compensation, the current at the end of the transmission line is far greater than its ampacity due to the large charging current, and it causes the core conductor temperature to exceed 90 ◦C, accelerating insulation aging. After reactive compensation, the current distribution on the transmission J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 15 of 18

720 0 MVar 700 50 MVar 114 MVar 680 Rating current 660

640

620

600 Current (A) Current

580

560

540

520

0 20 40 60 80 Cable length (km)

J. Mar. Sci. Eng. 2021, 9, 90 14 of 17 Figure 13. Comparison of current distribution of submarine cables under reactive power compensation at the sending end with the full-line ampacity under directly buried laying in landing section. J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEWline changes obviously. When the reactive power compensation amount at the sending 15 of 18 end is 50 MVar, the current at the receiving end of the line is still greater than the ampacity of thisAs section.shown When in thethe compensation figure above, at sending the end reachesdotted 114 line MVar, represents the current at the ampacity of different receiving end of the line decreases, while the current at sending end of the line increases. layingThe current sections distribution of long in the- linedistance does not exceedsubmarine the ampacity cables. of each The section. bottleneck point of submarine ca-

bles ampacity720 occurs in the landing section. When there is no reactive compensation, the 0 MVar current700 at the end 50 of MVar the transmission line is far greater than its ampacity due to the large 114 MVar 680 charging current, Ratingand currentit causes the core conductor temperature to exceed 90 °C, accelerating insulation660 aging. After reactive compensation, the current distribution on the trans- 640 mission line changes obviously. When the reactive power compensation amount at the 620

sending600 end is 50 MVar, the current at the receiving end of the line is still greater than the Current (A) Current ampacity580 of this section. When the compensation at sending end reaches 114 MVar, the current560 at receiving end of the line decreases, while the current at sending end of the line increases.540 The current distribution in the line does not exceed the ampacity of each section. 520

For0 the submarine20 40 cable60 transmission80 lines with a transmission distance greater than 90 km, the directly Cableburied length (km)laying method is adopted in the landing section. Only conduct- ingFigure reactive 13. Comparison compensation of current distribution at the of submarine sending cables end under of reactive the power line compensa- cannot meet the requirement of Figuretion 13. at Compa the sendingrison end of withcurrent the full-linedistribution ampacity of submarine under directly cables buried under laying reactive in landing power section. compensa- tionampacity. at the sending As end a result,with the full conducting-line ampacity underthe reactivedirectly buried compensation laying in landing section at mid. -line of the transmis- For the submarine cable transmission lines with a transmission distance greater than sion90 km,line the is directly considered. buried laying The method reactive is adopted inpower the landing compensations section. Only conducting are conducted at the sending andreactive Asreceiving shown compensation in endthe figures and at the above, the sending mid the end -dottedline of the at line line the represents cannot same meet time, the the ampacity requirementand the of calculation ofdifferent results are shown laying sections of long-distance submarine cables. The bottleneck point of submarine ca- in Figureampacity. 1 As4 a. result, conducting the reactive compensation at mid-line of the transmission bles lineampacity is considered. occurs The in the reactive landing power section. compensations When there are conducted is no reactive at the sendingcompensation, and the currentreceiving at the ends end and of the mid-linetransmission at the sameline time,is far andgreater the calculation than its ampac resultsity are due shown to inthe large Figure 14. charging current, and it causes the core conductor temperature to exceed 90 °C, accelerating insulation aging. After reactive compensation, the current distribution on the trans- 0 MVar mission620 line changes obviously. 50 MVar When the reactive power compensation amount at the sending end is 50 MVar, Rating the current current at the receiving end of the line is still greater than the ampacity600 of this section. When the compensation at sending end reaches 114 MVar, the current at receiving end of the line decreases, while the current at sending end of the line 580 increases. The current distribution in the line does not exceed the ampacity of each section. For the submarine cable transmission lines with a transmission distance greater than Current (A) Current 560 90 km, the directly buried laying method is adopted in the landing section. Only conducting reactive540 compensation at the sending end of the line cannot meet the requirement of ampacity. As a result, conducting the reactive compensation at mid-line of the transmission line520 is considered. The reactive power compensations are conducted at the sending and receiving ends and the mid-line at the same time, and the calculation results are shown 0 20 40 60 80 100 120 in Figure 14. Cable length (km)

Figure 14. Comparison of current distribution of submarine cables under reactive power compensation at mid-line with the full-line ampacity under directly buried laying in landing section. Figure 14. Comparison 0 MVar of current distribution of submarine cables under reactive power compen- 620 50 MVar sation atAccording mid-line toRating Figure with current 14 ,the when full the- submarineline ampacity cable transmission under directly line is 120 kmburied in length, laying in landing section. and600 the reactive power compensation is only carried out at the sending end of line, the current at the receiving end of the line is still far greater than its ampacity. Choose to conduct compensation580 of 114 MVar and 50 MVar at the sending end and mid-line respectively, and

Current (A) Current 560

540

520 0 20 40 60 80 100 120 Cable length (km)

Figure 14. Comparison of current distribution of submarine cables under reactive power compensation at mid-line with the full-line ampacity under directly buried laying in landing section.

J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 16 of 18

According to Figure 14, when the submarine cable transmission line is 120 km in J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 16 of 18 length, and the reactive power compensation is only carried out at the sending end of line, the current at the receiving end of the line is still far greater than its ampacity. Choose to conduct compensation of 114 MVar and 50 MVar at the sending end and mid-line respectively,According and the reactiveto Figure compens 14, whenation the forsubmarine receiving cable end transmission is applied to line meet is the120 requirementkm in length, and the reactive power compensation is only carried out at the sending end of line, of power factor. As shown in the figure above, conducting reactive power compensation the current at the receiving end of the line is still far greater than its ampacity. Choose to at mid-line can significantly reduce the current at receiving end, but it does not change conduct compensation of 114 MVar and 50 MVar at the sending end and mid-line respec- thetively, current and the distribut reactiveion compens from ationsending for receivingend to mid end-line. is applied It can to be meet considered the requirement as a reactive compensationof power factor. solution As shown for in thethe longfigure-distance above, conducting submarine reactive cable transmissionpower compensation lines if there J. Mar. Sci. Eng. 2021, 9, 90 areat mid sea- lineislands can significantlyin the middle reduce section the path current of lines. at receiving end,15 but of 17 it does not change the current distribution from sending end to mid-line. It can be considered as a reactive 5.2.compensation Cable Trench solution Laying for M theethod long in- Ldistanceanding Ssubmarineection cable transmission lines if there arethe sea reactive islands compensation in the middle for receiving section end is path applied of to lines. meet the requirement of power factor.As As shown in thein ﬁgureFigure above, 15 conducting, the cable reactive trench power laying compensation method at mid-line is adopted in the landing sec- tioncan signiﬁcantlyof the submarine reduce the currentcable transmission at receiving end, but lines it does with not a change transmission the current distance of 90 km. Com- pared5.2.distribution Cable with T fromrench the sending directlyLaying end M to buriedethod mid-line. in laying ItLanding can be method, considered Section asdue a reactive to the compensation better heat dissipation conditions solution for the long-distance submarine cable transmission lines if there are sea islands in inthe the middleAs cable shown section trench in path Figure ofand lines. smaller15, the cable environmental trench laying thermal method resistance, is adopted thein the calculated landing sec- ampacity tion of the submarine cable transmission lines with a transmission distance of 90 km. Com- is5.2. larger. Cable Trench The Laying ampacity Method inof Landing landing Section section with cable trench laying method is 582 A. When thepared sending with the end directly reactive buried compensation laying method, capacity due to thereaches better 88 heat MVar, dissipation the current conditions in the line in theAs cable shown trench in Figure and 15 ,smaller the cable environmental trench laying method thermal is adopted resistance, in the landing the calculated ampacity csectionan meet of the the submarine requirement cable transmission of ampacity. lines with In a transmissionFigure 16, distance the maximum of 90 km. transmission distance is larger. The ampacity of landing section with cable trench laying method is 582 A. When ofCompared the submarine with the directly cable buried transmission laying method, line due is to104 the km better when heat dissipationadopting the cable trench laying theconditions sending in the end cable reactive trench and compensation smaller environmental capacity thermal reaches resistance, 88 the MVar, calculated the current in the line modecampacityan meet in is the larger. requirementlanding The ampacity section, of of ampacity. landing and sectionthe In reactive withFigure cable 1power6 trench, the layingmaximum compensation method transmission is at sending distance end is 115 MVar,582 A. When which the sending can meet end reactive the requirement compensation capacity of ampa reachescity. 88 MVar, the current ofin the the linesubmarine can meet the cable requirement transmission of ampacity. line In Figureis 104 16 km, the when maximum adopting transmission the cable trench laying modedistance in of the the submarinelanding cablesection, transmission and the line reactive is 104 km whenpower adopting compensation the cable trench at sending end is 115 MVar,laying mode which in the can landing meet section, the requirement and the reactive of power ampa compensationcity. at sending end is 115 MVar, which can meet the requirement of ampacity.

Figure 15. Comparison of current distribution of 90 km submarine cables under reactive power com- pensationFigure 15. Comparison at the sending of current end distribution with the of 90 full km submarine-line ampacity cables under under reactive trench power com-laying in the landing section. Figurepensation 15. at Comparison the sending end of with current the full-line distribution ampacity under of 90 trench km submarine laying in the landingcables section.under reactive power compensation at the sending end with the full-line ampacity under trench laying in the landing section.

Figure 16. Comparison of current distribution of 104 km submarine cables under reactive power Figurecompensation 16.16. Comparison Comparison at the sending end of of withcurrent current the full-line distribution distribution ampacity underof 104 of trench 104km laying submarinekm insubmarine the landing cables section. cables under under reactive reactive power power compensation at at the the sending sending end end with with the the full full-line-line ampacity ampacity under under trench trench laying laying in the inlanding the landing section..

J. Mar. Sci. Eng. 2021, 9, 90 16 of 17

6. Conclusions This study considers a long-distance high voltage AC three-core submarine cable from a real offshore wind farm project. An accurate cable model is used to analyze the inﬂuence of reactive power compensation in different positions on the current distribution on the line, and optimizing the existing reactive power compensation schemes based on ETC. From the analysis, the following conclusions are obtained: (1) When the long-distance submarine cable is compensated for reactive power, not only the stability of the system should be maintained, but also the thermal limits of the submarine cable should be considered. The bottleneck of offshore wind farm output submarine cable ampacity appears in the landing section. (2) Conducting reactive compensation at sending end of the line can reduce the current at the receiving end. On the contrary, it can raise the current at the sending end of the line. The maximum current occurs at the sending or receiving end of the line depending on the capacity of reactive power compensation. (3) According to ETC, the current of long-distance submarine cable should be less than the ampacity under the condition of reactive power compensation. The cable trench laying method can improve the cable ampacity of landing section and thus reduce the capacity of reactive power compensation at sending end.

Author Contributions: Conceptualization, G.L., M.F., and P.W.; methodology, G.L.; software, M.F. and P.W.; validation, G.L., M.F., and P.W.; formal analysis, M.F. and P.W.; investigation, all authors.; resources, M.Z.; data curation, M.Z.; writing—original draft preparation, G.L. and M.F.; writing— review and editing, M.F. and P.W.; visualization, M.F. and M.Z.; supervision, G.L. and P.W.; project administration, M.Z.; funding acquisition, G.L. All authors have read and agreed to the published version of the manuscript. Funding: This work is the output of the research project “Life cycle cost analysis and evaluation of submarine power cables”[EX02061W], supported by Guangdong Electric Power Design Institute of Chinese Energy Engineering Group in Guangzhou. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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