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C5-3 10th International Conference on Insulated Power Cables C5-3

Jicable'19 - Paris - Versailles 23-27 June, 2019 1 / 6

Modeling of the Thermoelectric Performance of a ±320 kV HVDC Underground Cable System

Andreas I. CHRYSOCHOS, Nathanail CHYTIRIS, Konstantinos PAVLOU, Konstantinos TASTAVRIDIS, Georgios GEORGALLIS; Cablel® Hellenic Cables S.A., Greece, [email protected], [email protected], [email protected], [email protected], [email protected] Dimitrios CHATZIPETROS, Cablel® Hellenic Cables S.A., Greece, School of Electronics and Computer Science, Electrical Power Engineering Group, University of Southampton, UK, [email protected] ABSTRACT The thermoelectric performance of a ±320 kV HVDC un-derground cable system is examined by means of analyti-cal and FEM modeling. Both cable and joint geometry are investigated under steady-state and transient conditions, analyzing the different phases of a PQ test. Results facili-tate the theoretical assessment of the cable system actual performance prior to the real PQ test.

KEYWORDS Electric field, field inversion, HVDC cable system, PQ test.

INTRODUCTION HVDC solutions gain increasingly more ground in solidly insulated transmission lines because of their higher cost-effectiveness than the respective HVAC ones, particularly for long distances. Thanks to Voltage Source Converter (VSC) technology, XLPE insulated cable systems have al-ready been installed and are currently in operation.

In the present study, focus is made on the theoretical eval-uation of the combined thermoelectric performance of a ±320 kV underground cable system. First, the electric field distribution is considered in the cable, under a given tem-perature drop across the XLPE insulation layer. Due to its resistive nature, HVDC field is substantially different than that of a HVAC cable [1]. Results derived from analytical models existing in literature are presented, covering both steady-state and transient conditions. An improved numer-ical algorithm is proposed [2], [3], making the analytical models used more robust and stable under different oper-ating conditions. They are also compared against Finite El-ement Method (FEM) [4], showing a good agreement.

Since analytical methods are mostly limited to simple cylin-drical geometries, FEM is subsequently employed to simu-late the electric field distribution in more complex geome-tries such as a cable joint. Results in critical regions of the joint are shown, which are of importance before actual test-ing. The effect of inputs, such as the electrical conductivity of insulation, is also investigated [5].

FEM, including both electrical and thermal analyses, is then used in order to simulate the full heat cycles specified by IEC 62895 [6] and Cigré TB 496 [7] for a prequalification (PQ) test. Emphasis is given on the importance of the am-bient conditions which have to be considered in order to control the temperature difference over the cable insula-tion. Time-dependent thermal and electrical profiles are presented. These provide in advance the designer with a full theoretical assessment of the actual performance of the whole cable system which is going to be later PQ tested. Finally, the electrical behavior under impulse voltage is modeled and investigated.

THEORETICAL BACKGROUND In this section, the theoretical background for the calcula-tion of the electric field distribution is presented under both transient and steady-state conditions. The generic formula-tion can be applied to any arbitrary geometry, while it is sig-nificantly simplified in cases of axisymmetric geometry.

Transient electric field distribution Contrary to HVAC cables, the electric field under DC stress is temperature and time dependent. This is attributed to the resistivity of the dielectric medium which depends on tem-perature and electric field [1]. The transient electric field distribution can be described by the following equations:

Jtρ∂

∇ ⋅ = −∂

(1)

J Eσ=

(2)

E V= −∇

(3)

( )Eε ρ∇ ⋅ =

(4)

where J

the current density, E

the electric field, ρ the space charge density, V the voltage potential, σ the dielec-tric conductivity, and ε the dielectric permittivity.

Due to the absence of any comprehensive theoretical model for the conduction in polymeric materials, the dielec-tric conductivity is usually described by the following empir-ical expression [1]:

( ) ( )0

ref refα T T β E Ee eσ σ − −= (5)

where σ0 the dielectric conductivity at reference tempera-ture Tref and electric field Eref, and α, β the temperature and field coefficient of dielectric conductivity, respectively.

In order to calculate temperature T in (5), the heat transfer problem must be solved, which for transient conditions in solid medium is given by:

2P

TdC k T Qt

∂+ ∇ =

∂ (6)

where d, CP and k the material density, heat capacity at constant pressure and thermal conductivity, respectively, while Q the external heat source including also the resistive heating by leakage current on dielectric medium.

Steady-state electric field distribution The steady-state electric field distribution can be calculated by simplifying (1) and (6) to:

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0J∇ ⋅ =

(7)

2k T Q∇ = (8)

while solving the remaining equation set of (2)-(5).

CABLE GEOMETRY Since the electric field is confined between conductor and sheath, only the cable insulation is modeled as shown in Fig. 1. The inner radius ri is under voltage potential Vi and temperature Ti, while the outer radius ro is assumed grounded at temperature To.

Anode(+)

ri, Vi, Ti

Cathode(-)

ro, Vo, To

r

ε, σd, CP, k

Fig. 1: Geometry of cable insulation.

The electric field is calculated both in transient and steady-state conditions based on the fact that the leakage current loss within dielectric is negligible. In addition, it is assumed that the dielectric medium does not present any chemical or physical defects, while no charge carriers is injected by the electrodes [1].

Steady-state conditions The equation set of (2)-(5), (7) and (8) is solved by exploit-ing the cylindrical geometry of Fig. 1. The heat transfer problem of (8) leads to:

ln2

C oi o

i

W rT T Tk rπ

∆ = − =

(9)

where WC the per length conductor Joule loss.

Eoll’s analytical approximation The remaining equations are solved by starting from Ohm’s law in (2), yielding the electric field distribution at any point with radial distance r. The following approximation for the exponential term is adopted [8]:

( )0rβE

re E E τ−− ≅ (10)

where i

o i

βVr r

τ =−

and ( )0i

o i

VEe r r

=−

.

By applying (10), an analytical solution for the electric field can be derived [8]:

1

1

δ

io

r δi

oo

rVδ rE

rr r

− =

−

(11)

where 1

γδ = ττ++

and 2

CαWγkπ

= .

Eq. (11) can be solved in a straightforward manner giving

a solution rapidly. However, its accuracy depends largely on the validity of the approximation in (10).

Direct numerical calculation Another approach for the solution of set (2)-(5) and (7) is to start from the fundamental electrical circuit theory. Within this context, the final formula of electric field is given by [9]:

1

1

r

o

r

i

βEsi

r rβEs

r

V r eEr e dr

−−

−−

=

∫ (12)

where ( )ln o i

αΔTsr r

= .

Eq. (12) provides a more accurate calculation of electric field compared to (11), since it does not require the approx-imation of (10). However, it can only be solved numerically using a computer-based method.

Gauss-Seidel iterative method

In [10] it is proposed to solve (12) using Gauss-Seidel iter-ative method. In this case (12) is rewritten as:

1

1 1

1

nr n

r

onr

i

βEsβEn si

r rβEs

r

V r eE Ar er e dr

−−−+ −

−−

= =

∫ (13)

where n denotes the iteration counter.

Eq. (13) is iteratively solved with the denominator being ap-proximated by using (11). The convergence requirement is met when 1n n

r rE E tol+ − < , where tol is a user-defined con-

verge limit, e.g. 1 V/mm. The initial guess 0rE is calculated

by setting β = 0 in (12).

Levenberg-Marquardt iterative method

Although (13) provides a more accurate calculation of elec-tric field compared to (11), it was found through many cal-culation examples that its iterative scheme is not always numerically stable. As a result, another calculation scheme for the numerical evaluation of (12) is proposed in this pa-per based on the Levenberg-Marquardt iterative method [2], [3]. Within this context, (12) is reformulated as:

( ) ( ) ( ) ( )11 1n n n n nr r r r rE E λ H E J E F E

−+ = − + (14)

where:

( )1

1

nr

onr

i

βEsn n ir r r

βEs

r

V r eF E Er e dr

−−

−−

= −

∫ (15)

while ( )nrJ E and ( )n

rH E are the Jacobian and Hessian

forms of ( )nrF E , i.e. the first and second order derivatives.

The positive scalar combination coefficient λ controls both the magnitude and direction of 1n n

r rE E+ − in (14). Starting from a small value, e.g. 10-4, λ is consecutively adjusted in order to ensure the decrease of (15) in each iteration. If

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( )nrF E of the next iteration step is decreased, it implies

that the quadratic assumption is satisfied and λ is reduced by a factor of 10 in order to reduce the influence of the gra-dient descent. On the other hand, if ( )n

rF E is increased, λ

is increased by the same factor so as to follow more the direction of the gradient. A lower limit of λ, e.g. 10-15, is also set in order to avoid floating-point overflows. The algorithm iterates until (15) becomes smaller than the tolerance err, typically set to 10-6 or less. The initial guess 0

rE is calcu-lated using (11).

Results A cable with dielectric inner and outer radii of 30 mm and 52 mm is examined. The cable is subject to a DC voltage of 320 kV, while coefficients α, β of (5) are equal to 0.101 K-1 and 0.0775 mm/kV [5], respectively. Results of steady-state electric field distribution are shown in Fig. 2 for varying temperature difference ΔT of (9). The proposed method is compared to Eoll’s approximation and Gauss-Seidel method when applicable. FEM calculation based on (2)-(5), (7) and (8) is also shown, which is considered as reference. In addition, Laplacian field is plotted for compar-ison reasons.

Results show the high dependence of field with tempera-ture, leading to field inversion after a certain value of ΔT. Eoll’s approximation is in good agreement with the corre-sponding of FEM for small ΔT. However, for higher ΔT, de-viations are observed due to the non-validity of the approx-imation in (10). The Gauss-Seidel method is characterized by unstable behavior, since convergence is only suc-ceeded for the case of 5 K. On the other hand, the pro-posed methodology is robust in all examined cases, while being also in very good agreement with FEM.

LaplaceEollLMFEMGauss-Seidel

Fig. 2: Steady-state electric field distribution.

Transient conditions Eqs. (1)-(6) are employed for the calculation of electric field distribution in transient conditions. First, the heat transfer problem of (6) is solved by employing the methodology of [11], where the cable is simulated using a thermal ladder network. Each cable layer, along with the surrounding soil, is divided into elementary layers, where the temperature Tr,t, is space and time dependent.

Then, the electric field distribution is calculated by simplify-ing (1)-(5) due to cylindrical geometry and by applying first-order differences [5]:

, ,, ,

, , ,

r t r tr t t r t

r t r t r t

tJ

t tσ ερ ερ

σ ε σ σ+∆

∆= + ∇ ∆ + ∆

(16)

,

,,

11

ln

o

i i

i

r rr t t

i rr R r t t

r t tro

i

rV dr dr

r rE dr

rrrr

ρε ρ

ε

′ +∆

′ +∆+∆

′′ − ′ ′= +

∫ ∫∫ (17)

( ) ( ), ,, 0

r t t ref r t t refα T T β E Er t t e eσ σ +∆ +∆− −

+∆ = (18)

, , ,r t t r t t r t tJ Eσ+∆ +∆ +∆= (19)

The calculation procedure at each radial distance r and time instant t is based on (16)-(19) following the flowchart of Fig. 3.

Calculate Tr,t for rϵ[ri,ro] and t ϵ [0,ttot] based on [11]

Initialize ρr,0, Er,0, σr,0 and Jr,0 at n=0

Time step t=t+Δt

Iteration n=n+1

Update ρr,t(n), Er,t(n), σr,t(n) and Jr,t(n)

Calculate new ρr,t(n) from (16)Calculate new Er,t(n) from (17)Calculate new σr,t(n) from (18)Calculate new Jr,t(n) from (19)

Max[Abs(Er,t(n),n-Er,t(n),n-1)] < tol

tn < ttot

Start

End

No

Yes

No

Yes

Fig. 3: Flowchart for transient calculation.

Results As an indicative numerical example, the cable is subject to a simultaneous voltage and current step function of 320 kV and 2650 A, respectively [9]. The methodology of Fig. 3 is compared to FEM based on (1)-(6). In Fig. 4 the tempera-ture and electric field responses along a day are shown for the inner and outer insulations radii. Results are in very good agreement, validating the methodology of Fig. 3.

JOINT GEOMETRY The analytical and numerical tools presented in the previ-ous section are sufficient for field calculations when sym-metrical geometries are under consideration that permit 1D analysis. However, when non-symmetrical geometries have to be studied, such as a cable joint, FEM becomes mandatory, since it can implement 2D analysis.

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Fig. 4: Temperature and electric field transient re-

sponse.

Having first verified the FEM results against those obtained from the existing analytical methods, such as shown in Figs. 2 and 4, FEM is extended in the present section for a 320 kV joint with a 2500 mm2 Cu conductor. Heating Cycle (HC) and Switching Impulse (SI) FEM models are devel-oped, so as to simulate the corresponding tests. The test conditions specified by IEC 62895 [6] are taken into con-sideration, focusing on the PQ requirements.

Heating Cycle (HC) model PQ tests include several 24 h HCs, while the whole cable system is under DC test voltage UTP1 = 1.45U0. The first 4 HCs are considered in the present section for simplicity, in-cluding 8 h heating and 16 h natural cooling. The modeling assumptions adopted are presented first; the effect of α, β parameters on the derived results is then discussed; finally, the variation in external ambient conditions is considered and the relevant impact on the maximum temperature drop over the cable insulation, ΔTmax, is discussed.

Modeling aspects A common joint type contains EPDM for joint insulation [12]. An indicative 2D geometry is shown in Fig. 5. Due to symmetry with respect to z = 0 plane, ½ geometry is ade-quate to be modeled, provided that the necessary bound-ary condition of symmetry is applied at the down end. Fur-thermore, end effects are eliminated through a coordinate scaling which virtually extends the upper edge towards in-finity. An AC current is then applied to the conductor such that the maximum conductor temperature Tcond,max reaches a value between 70 and 75 °C. Additionally, the loss gen-erated by the leakage current across both cable and joint insulations is considered by coupling the thermal with the electrical model, i.e. by including as a heat source the re-sistive heating due to leakage current in the right hand of (6). Finally, constant voltage potentials equal to UTP1 and 0 are imposed on the outer conductor and EPDM surfaces, respectively. Eqs. (1)-(6) are eventually solved by FEM.

Effect of the selected α, β parameters set Two parameter sets for XLPE conductivity [5] are studied in this section, as shown in Table I. One set is considered for EPDM for the sake of brevity. 4 HCs are simulated per set, assuming natural convection and radiation on the outer surface of the joint with an ambient temperature of 20 °C. Conductor temperature response Tcond is extracted in com-mon axes with the electric field, i.e. Ei and Eo at the inner and outer cable insulation surface, respectively.

Fig. 5: Joint geometry.

TABLE I

Sets for temperature and field coefficients.

Set XLPE EPDM α (K-1) β (mm/kV) α (K-1) β (mm/kV)

1 0.042 0.032 0.1 0.09 2 0.101 0.0775 0.1 0.09

As shown in Figs. 6 and 7, Tcond is kept sufficiently higher than 70 °C and within a tolerance of -0 K +5 K, being in alignment with [6]. Ei and Eo present similar initial values for both sets, which can be attributed to the capacitive na-ture of the electric field that dominates when the joint is kept at ambient temperature. However, they show fairly different trends when time increases and a temperature drop ΔT gradually applies on the cable insulation: Ei > Eo for about 60% out of the total HC duration, while Ei < Eo (field inver-sion) for about 40% in terms of Set 1 (Fig. 6); instead, Ei < Eo (field inversion) happens for about 60% out of the total HC duration in terms of Set 2 (Fig. 7). Additionally, maximum Eo appears to be higher than the initial Ei value for the latter set. This fact might push the cable insulation besides its capacitive acceptable limits, making more pos-sible a failure during testing.

Fig. 6: Tcond and Ei, Eo against time - Set 1.

0 200 400 600 800 1000 1200 1400Time [min]

20

30

40

50

60

Tem

pera

ture

[o

C]

(a)

Ei - Num. E

i - FEM E

o - Num. E

o - FEM

0 200 400 600 800 1000 1200 1400Time [min]

0

5

10

15

20

Elec

tric

field

[kV/

mm

]

(b)

Conductor (Cu)

Cable Insulation (XLPE)

Joint Insulation (EPDM)

Deflector (Semicon PE)

z-axis

r-axis

Connector (Metal Alloy)

0 8 16 24 32 40 48 56 64 72 80 88 96Time [h]

20

30

40

50

60

70

80

Tem

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ture

[o

C]

0

5

10

15

20

25

30

Elec

tric

field

[kV/

mm

]

Tcond

Ei

Eo

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Fig. 7: Tcond and Ei, Eo against time - Set 2.

Next, the interface between cable and joint insulation (XLPE - EPDM) is examined, where the tangential electric field Etang is plotted for several time points of the 4th HC. Etang distributions along XLPE - EPDM interface present a similar trend for both sets, as shown in Fig. 8. Higher values are noticed in the beginning of the load step, with the peak being located close to deflector; smoother distributions occur during joint heating due to the resistive nature of the electric field. Etang values are restored back to the initial dis-tribution as soon as the HC is completed. By comparing Figs. 8(a) and 8(b), higher values occur in terms of Set 1, implying that in this case the interface might be more vulnerable if insufficient mechanical pressure is applied between XLPE and EPDM.

Fig. 8: Etang along XLPE – EPDM interface. (a) set 1

and (b) set 2.

Effect of the ambient conditions Besides the electrical performance studied for a given pa-rameter set, predicting ΔTmax across the net cable insula-tion during HC simulations is also important for HVDC ca-ble systems. ΔTmax has to be recorded during the actual cable testing, as specified by [6]; thus, an in advance esti-mation of ΔTmax is useful. The actual Tcond,max is expected close to the center of joint, where the thermal resistance is higher. Although it is rather difficult to take temperature measurements at that point, Tcond,max can be derived from FEM simulations. Set 1 is used in this section, while tem-perature and electric field results are presented for different ambient conditions: Natural convection is applied on the external joint surface with Tamb equal to 20 °C and 30 °C (Cases 1 and 2, respectively); forced convection with Tamb = 20 °C and an indicative air velocity v = 4 m/s (Case 3) is also considered. Surface radiation is assumed in all exam-ined cases. Ei, Eo results in terms of Case 1 are omitted for brevity, since they have been shown in Fig. 6.

ΔTmax shall be maintained during at least the last 2 h of the

heating period, as remarked by [6]. Results in Figs. 9 and 10 suggest ΔTmax ≈ 26 °C and 21 °C, respectively. As expected, ΔΤmax decreases when Tamb increases, since lower conductor current is required so as to achieve the same Tcond,max. Therefore, different ΔΤmax will occur if the cable testing takes place in different climate conditions. In-stead, higher ΔΤmax values may be reached for more ther-mally favorable conditions, as seen in Fig. 11 (ΔΤmax ≈ 35 °C). Hence, by varying ambient conditions, ΔΤmax can be controlled. The control of ΔΤmax by means of a “water jacket” is presented in [13] and [14].

Fig. 9: Tcond, Tsurf and ΔT VS time - Case 1.

Fig. 10: Tcond, Tsurf and ΔT VS time - Case 2.

Fig. 11: Tcond, Tsurf and ΔT against time - Case 3.

On the other hand, when ΔΤmax overly increases, Ei < Eo (field inversion) for longer time spans, as shown by com-paring Figs. 12a and 12b. Thus, some compromise has to be adopted in order to keep Ei and Eo lower than the design stress levels and, simultaneously, ensure the ΔΤmax be suf-ficiently higher than that expected under the actual installa-tion conditions.

0 8 16 24 32 40 48 56 64 72 80 88 96Time [h]

20

30

40

50

60

70

80

Tem

pera

ture

[o

C]

0

5

10

15

20

25

30

Elec

tric

field

[kV/

mm

]

Tcond

Ei

Eo

0 50 100 150 200 250 300 350

Spatial distance [mm]

0

1

2

3

4

5

6

Tang

entia

l ele

ctric

fiel

d [k

V/m

m]

(a)

t = 72 ht = 78 ht = 80 ht = 88 ht = 96 h

0 50 100 150 200 250 300 350


0

0.5

1

1.5

2

2.5

3

3.5

4

Tang

entia

l ele

ctric

fiel

d [k

V/m

m]

(b)

0 8 16 24 32 40 48 56 64 72 80 88 96Time [h]

20

30

40

50

60

70

80

Tem

pera

ture

[o

C]

-5

0

5

10

15

20

25

30

Tem

pera

ture

[o

C]

Tcond

- left

Tsurf

- left

T - right

0 8 16 24 32 40 48 56 64 72 80 88 96Time [h]

30

35

40

45

50

55

60

65

70

75

80

Tem

pera

ture

[o

C]

0

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15

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25

Tem

pera

ture

[o

C]

Tcond

- left

Tsurf

- left

T - right

0 8 16 24 32 40 48 56 64 72 80 88 96Time [h]

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Tem

pera

ture

[o

C]

0

5

10

15

20

25

30

35

40

Tem

pera

ture

[o

C]

Tcond

- left

Tsurf

- left

T - right

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Fig. 12: Ei, Eo against time - Cases (a) 2 and (b) 3.

Switching Impulse (SI) model After the HCs are completed, the superimposed switching impulse (SI) voltage test shall be performed as specified in [6]. The aim of such a test during PQ testing is to check the integrity of the cable system. As cited in [6], Tcond ≥ Tcond,max and ΔT ≥ ΔTmax shall be reached for at least 10 h before the first SI is applied and shall be maintained during the duration of the test. In other words, steady-state conditions regarding both the thermal and electric fields are to be achieved before the SI test.

Eqs. (2)-(4), (7), and (8) are first solved by means of FEM. Then, (1) is additionally solved, while the waveform for the SI excitation (250 μs/ 2500 μs) is approached by a double exponential function with amplitude UP2,O = 1.2U0. Set 1 pa-rameters are again assumed. Etang between XLPE - EPDM is depicted in Fig. 13 for several time points before and af-ter peak time.

Fig. 13: Etang along XLPE – EPDM interface – Set 1 (SI).

The maximum field value is located on the outer surface of deflector. Maximum Etang shown in Fig. 13 is noticed at peak time instant, as expected. It should be noted that ac-tual field values become negative where Etang appears to meet x-axis: This is because the norm of Etang is extracted from FEM and shown in Fig. 13. Finally, the capacitive na-ture of SI should be underlined, as also pointed out in [1]: Identical results in terms of maximum electric field can be obtained if an electrostatic analysis was attempted instead of the transient approach, i.e. by using (3) and (4) with the term on the right hand of (4) being null and assuming a po-tential equal to UP2,O.

CONCLUSIONS In this paper, a thorough thermoelectric performance of a ±320 kV HVDC underground cable system is presented.

The electric field is first calculated for a cable geometry us-ing new numerical methods, while it is validated against FEM. Steady-state and transient conditions are studied in terms of both thermal and electric fields. Next, a joint is ex-amined by theoretically assessing its performance during a PQ test with the aid of FEM. Results facilitate the designer during the development phase of HVDC cable and acces-sories.

REFERENCES

[1] G. Mazzanti, M. Marzinotto, Extruded cables for high-voltage direct-current transmission, IEEE Press and Wiley, New Jersey, USA, 2013.

[2] K. Levenberg, “A method for the solution of certain problems in least squares,” Quart. Appl. Math., vol. 2, 1944, pp. 164-168.

[3] D. Marquardt, “An algorithm for least-squares estima-tion of nonlinear parameters,” SIAM J. Appl. Math., vol. 11, no. 2, 1963, pp. 431-441.

[4] COMSOL Multiphysics®, v.5.4, www.comsol.com, COMSOL AB, Stockholm, Sweden.

[5] G. Mazzanti, “Including the calculation of transient electric field in the life estimation of HVDC cables sub-jected to load cycles”, IEEE Elect. Insul. Mag., vol. 34, no. 3, 2018, pp. 27-37.

[6] IEC standard for high voltage direct current (HVDC) power transmission - Cables with extruded insulation and their accessories for rated voltages up to 320 kV for land applications - Test methods and requirements, IEC Standard 62895, 2017.

[7] CIGRE recommendations for testing DC extruded ca-ble systems for power transmission at a rated voltage up to 500 kV, CIGRE 496, 2012.

[8] C. Eoll, “Theory of stress distribution in insulation of high-voltage dc cables: Part I,” IEEE Trans. Electr. Ins., vol. EI-10, no. 1, 1975, pp. 27-35.

[9] M. Jeroense, “Charges and discharges in HVDC ca-bles: In particular in mass-impregnated HVDC cables”, Ph.D. dissertation, Delft University, Delft, Netherlands, 1997.

[10] Z. Huang, “Rating methodology of high voltage mass impregnated DC cable circuits”, Ph.D. dissertation, University of Southampton, Southampton, UK, 2014.

[11] ELECTRA computer method for the calculation of the response of single-core cables to a step function ther-mal transient, ELECTRA 87, 1983.

[12] H. Ye, T. Fechner, X. Lei, Y. Luo, M. Zhou, Z. Han, H. Wang, Q. Zhuang, R. Xu, D. Li, “Review on HVDC ca-ble terminations,” IET High Volt., 2018, pp. 79-89.

[13] A. Tzimas, G. Lucas, K. J. Dyke, F. Perrot, L. Boyer, P. Mirebeau, S. Dodd, J. Castellon, P. Notingher, 2015, “Space charge evolution in XLPE HVDC cable with thermal-step-method and pulse-electro-acoustic”, Jicable’15, Paris, France, June 21-25, 2015.

[14] A. Tzimas, G. Lucas, K. J. Dyke, F. Perrot, Y. Yagi, H. Tanaka, S. Dodd, 2015, “Space charge evolution in composite XLPE HVDC cable insulation during VSC pre-qualification programme”, Jicable’15, Paris, France, June 21-25, 2015.

0 16 32 48 64 80 96Time [h]

0

5

10

15

20

25

30

Elec

tric

field

[kV/

mm

]

(a)

Ei

Eo

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0

5

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20

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field

[kV/

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0 50 100 150 200 250 300 350


0

0.5

1

1.5

2

2.5

3

3.5

Tang

entia

l fie

ld [k

V/m

m]

t = 125 μst = 250 μst = 375 μst = 5000 μs

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