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3-LO-SP2-06S

Superconducting Cable Modelling into Electro-

Magnetic Transient Simulation Tool
Christophe Creusot, Antonio Morandi Senior Member, IEEE, Francesco Mimmi, Emiliano Guerra, Alberto
Bertinato, Pierre-Baptiste Steckler, Pier Luigi Ribani, Massimo Fabbri, Marco Bocchi, Andrea Musso,
Giuliano Angeli, Diego Brasiliano

Abstract —The European project SCARLET aims to study and is designed to be a hybrid energy transportation link combining
realize a demonstrator of a MVDC (Medium Voltage Direct electrical power transportation as well as hydrogen chemical
Current) high-power superconducting cable. This device might be energy transportation [3].
employed to connect offshore wind farms with land, expecting to
significantly simplify the offshore platform by eliminating the need DC cable designs and constraints have been presented by
for its conversion function. For this purpose, windmill conversion different authors, mainly describing their architecture and their
chain must be modified to directly produce the MVDC export thermal and electric insulation systems [4]-[9]. The response to
voltage. a fault has been addressed in [5]-[8]. A ±100 kV DC system
In this scenario, this paper presents the case of a 1GW offshore including HTS power cable has been modelled in fault
windmill superconducting link and outlines the design conditions in [7] and [8], considering a point-to-point and a
consideration for a 1 GW onshore converter. For this cable, a
multi-terminal layout respectively.
protection strategy that combines DC circuit breakers with a
Resistive Superconducting Fault Current Limiter is proposed. This article will describe the main technological components
Moreover, this works demonstrates how a superconducting cable necessary to ensure the safe operation of the superconducting
can be modelled as an electrical circuit to be integrated into a cable at medium voltage level, considering a 1 GW level of
network simulation tool, enabling the investigation of various fault electrical power transmission. Additionally, it will discuss the
scenarios and protection strategies. Finally, a specific result is electrical modeling of the superconducting cable and how it can
discussed to exemplify how the proposed approach can benefit the
be implemented into the commercial software EMTP® [10]-
design of both the electrical network and the superconducting
cable itself. [11], which is specialized and commonly used for the
simulation of transients in distribution or transmission grids, to
Index Terms — Cables, Converter, Modelling, MVDC, Protection, evaluate the interaction between the DC system and the cable
Superconductivity itself.

II. REFERENCE CASE FOR 1 GW DC TRANSMISSION WITH

I. INTRODUCTION SUPERCONDUCTING CABLES

I N the framework of the European project SCARLET [1],

the use of superconducting (SC) cables either onshore or
offshore is being investigated for various application cases
[2]. The main objective is to leverage the benefits of conducting
large currents, typically exceeding 10 kA, while alleviating
One of the primary objectives of the SCARLET project is to
demonstrate the feasibility of exporting bulk offshore wind
power to onshore locations using a medium voltage DC
superconducting cable. The main advantage of this approach is
the ability to eliminate the offshore conversion platform. To
high voltage constraints by operating at medium DC voltage achieve this, modifications are required to convert the existing
(typically below 100 kVdc). Specifically, two superconducting AC output of the windmill into a DC output. This is feasible as
cable technologies are being designed and will be brought to the the windmill already contains a conversion chain that can be
demonstration level: one utilizing High-Temperature adapted to produce the required DC voltage.
Superconductor (HTS) tapes, operating at ±50 kVdc and cooled The greater challenge lies in transforming the onshore HVDC
with liquid nitrogen, and the other using Magnesium Diboride conversion station into an MVDC station. The current HVDC
(MgB2) wires, operating at ± 25 kVdc and cooled with liquid converters are limited in their nominal current ratings by
hydrogen. The HTS superconducting cable will not only be individual components (IGBTs or IGCTs). In fact, due to the
designed for onshore applications but also for offshore use, current constraints imposed by conventional cables, enhancing
considering a typical subsea length of 100 km. The MgB2 cable transmission power necessitates an elevation in voltage up to

The SCARLET project has received funding from the European Union’s A. Morandi, F. Mimmi, E. Guerra, P. L. Ribani and M. Fabbri are with the
Horizon Europe research and innovation programme under grant agreement University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy (e-
No. 101075602. (Corresponding author: Christophe Creusot). mail: antonio.morandi@unibo.it, francesco.mimmi2@unibo.it,
C. Creusot, A. Bertinato, P.-B. Steckler and D. Brasiliano are with emiliano.guerra5@unibo.it, pierluigi.ribani@unibo.it,
SuperGrid Institute, 69100 Villeurbanne, France (e-mail: massimo.fabbri@unibo.it).
christophe.creusot@supergrid-institute.com, alberto.bertinato@supergrid- M. Bocchi, A. Musso and G. Angeli are with RSE S.p.A., Via Rubattino 54
institute.com, pierre-baptiste.steckler@supergrid-institute.com, 20134 Milan, Italy (e-mail: marco.bocchi@rse-web.it, andrea.musso@rse-
diego.brasiliano@supergrid-institute.com). web.it, giuliano.angeli@rse-web.it)
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525 kVdc in Europe [11]. The practice involves connecting a resulting in a short circuit duration on the order of 60 ms.
larger number of modules in series, effectively increasing the Another significant advantage of the RSFCL is its ability to
transmission voltage. regenerate much faster than the SC cable in case it is not present
For the ±50 kVdc case, the proposed approach is to and the fault results in a SC cable quench.
implement four Modular Multilevel Converters (MMC) in The schematic of the proposed 1 GW offshore export system
parallel, each of them fed by a 3-Phase transformer, as shown is depicted in Fig. 2. Windmill clusters are of 200 MW size,
in Fig. 1. This setup naturally facilitates the converter protection they are connected to the DC busbar via medium voltage
by employing a DC breaker with a series reactor on the DC side resistive cables. Possibly, one DC breaker can be installed at
and an AC breaker on the AC side. This configuration allows each cluster, allowing a continuous power flow in case a failure
occurs in one cluster.

III. CIRCUIT MODEL OF SUPERCONDUCTING CABLES

In this paper, an equivalent circuit model for the cable and its
integration into EMTP® has been developed. This integration
also encompasses the model of the DC system to evaluate their
overall behavior, which is significantly influenced by their
mutual interaction.
In the following, the model of the reference ±50 kVdc – 10
kA DC HTS cable is described in detail. The same modelling
Fig. 1. Unifilar Onshore 1 GW ±50 kVdc converter station scheme. approach also applies to the ±25 kVdc – 20 kA DC MgB2 cable.
The layout of the reference cable is schematically shown in Fig.
for the elimination of a fault in one converter while maintaining 3, it comprises a wired copper former, four HTS layers
power transmission through the non-faulty converters. consisting of helically wound 2G tapes, and a stranded copper
DC circuit breakers are a subject of ongoing research in the shield. Low-conductivity carbon black wrapping, indicated in
HVDC field worldwide, with various manufacturers offering black in Fig. 3, is included between all layers. Electrical
solutions. The solution presented in this study is a mechanical insulation is placed between the outer HTS layer and the copper
circuit breaker with active high-frequency current injection. It shield. The cable core is enclosed within a cryostat with two
is based on 35 kV modules, so for the ±50 kVdc application, metallic pipe walls.
two modules are connected in series, while for the ±25 kVdc, To develop the equivalent circuit, each of the physical
only one module is necessary. Laboratory tests have conductors of the cable (HTS tapes, copper wires or tapes in the
demonstrated its capability to interrupt a current of up to 20 kA. former and in the shield) is first individually modelled. A
Thanks to its electromagnetic actuator, it achieves a fault reduction procedure of the number of circuit components is
neutralization time of less than 5 ms [13]. later applied before implementing the circuit in EMTP®
The fast-acting DC breaker is advantageous for minimizing environment. The model of each individual conductor consists
stress on the SC cable in case of a fault. Additionally, it is of a resistor in series with an inductor. All individual inductors
proposed to install a Resistive Superconducting Fault Current are coupled with each other. The calculation of the induction
Limiter (RSFCL) in series with the SC cable. The RSFCL will coefficients is based on the precise geometrical model of the
absorb a significant amount of energy before fault helical conductors, as described later. Metallic pipes of the
neutralization by the DC circuit breakers. Its protective role cryostat are also included in the model by assuming that they
becomes even more crucial in the event of DC breaker failure, only carry current in the longitudinal direction and by splitting
where fault current interruption would rely on AC breakers, them in a set of straight tile-shaped conductors parallel to the

Fig. 2. Complete reference case schematic (DC bifilar and AC unifilar).

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Fig. 3. Reference layout of the HTS cable.

Fig. 5. Inductance per unit length HTS tapes of the first layer as a function of
the axial length in the range 0.2 m (1 twist pitch) to 200 m (1000 twist pitches).

performed using a semi-analytical approach. More in particular,

each of the tapes is divided into several thin filaments, whose
axes are further subdivided into a number of straight segments.
Grover’s formula is employed to calculate the partial
inductance between the two straight segments [14]. The final
value of the inductance is obtained through a double summation
over the filaments and the segments of the subdivision.
As an example, Fig. 5 shows the self-inductance per unit length
of one HTS tape of the first layer as a function of the axial
length of the helix, ranging from 1 twist pitch (L0 = 0.2 m) to
1000 twist pitches (200 m). The presented inductances per unit
length are normalised with respect to their corresponding axial
length. The same plot also shows the mutual inductance per unit
length between one HTS tape of the first layer and one HTS
tape of the second layer displaced by 90 degrees with respect to
the former one.
An exact logarithmic increase of the calculated inductances per
Fig. 4. Electro-thermal model for a section of the HTS cable, defined by its unit length m with respect to the length L can be observed from
length (L), using individual conductor models. (a) Electric Circuit and (b) Fig. 5, which can be interpolated by means of:
Thermal Network.
𝐿
cable. In Fig. 4a, the electric circuit model for individual 𝑚 = 𝑚0 + 𝑘 𝑙𝑛 ( ) [H/m] (1)
𝐿0
conductors is presented. This schematic depicts a cable section
with a designated length (L), where each individual tape or wire where L0 is the twist pitch and m0 and k are fitting
is modelled as an insulated conductor. The electric circuit coefficients. Verification has been performed through
consists of clusters of parallel R-L branches representing all numerical calculations to ensure that the logarithmic trend is
conductors for each cable’s component (former, HTS layers, strictly obeyed by any induction coefficient (self- or mutual-)
shield and pipes). The capacitive coupling between the outer of the conductors of the cable. This means that for calculating
HTS layer and the shield (through electric insulation), between the self-induction coefficients M of each cable conductors (or
the shield and the inner pipe (through coolant), and between the the mutual induction coefficients between pairs) of any length,
inner and outer pipe (through vacuum) is also included in the only the fitting parameters m0 and k must be determined. Thus,
model. the inductance M can be obtained from the Eq. (2):
Since all circuit resistances are temperature-dependent, a
coupled thermal network, shown in Fig. 4b, is introduced to 𝑀 = 𝐿𝑚 = 𝐿𝑚0 + 𝑘 𝐿𝑙𝑛 ( ) [H]
𝐿
(2)
𝐿0
calculate the time evolution of all conductors’ temperatures
based on the dissipation of the electric circuit. In the remainder
To obtain the inductance coefficients, the self and mutual
of this Chapter, the parameters of the circuit model for
inductances per unit length of all the conductors of the cable
individual conductors and the thermal network will be
were plotted against the axial length over an interval ranging
described in Sections A, B, and C. Finally, in Section D, the
from 1 to 10 twist pitches (that is, from 0.2 m to 2 m). Fitting
reduction procedure of the circuit is discussed. parameters m0 and k were then obtained from these plots and
used for calculating the inductance coefficients relative to the
A. Inductances considered cable length via Eq. (2). Simplifying symmetry
The calculation of the mutual- and self-inductance conditions were adopted (for example, the self-inductances of
coefficients of helically wound tapes (or wires) has been all tapes of a layer were considered to be identical, as well as
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3-LO-SP2-06S
mutual inductance between adjacent tapes in the same layer, where Ceq is the equivalent thermal capacity of the conductors
etc…). For the reference cable layout of Fig. 3, 182 conductors and, on the right side of Eq. (7), the dissipation term is
are included in the model, consisting of all the copper wires of implemented in the form of a controlled current source. The
the former, all the tapes of the HTS layers, all the copper tapes temperature of each conductor corresponds to the ground
of the shield, and all the straight tile-shaped conductors used for potential of the circuit nodes common to fictious capacitances
modelling the metallic pipes (each split in 24 straight and current source that are highlighted in Fig. 4b. For the
conductors). The total calculation time of the full, symmetric, purposes of the thermal network, the HTS tapes are modelled
182182 inductances matrix was about 6 hours. as a homogeneous material with an equivalent thermal capacity
given by:
B. Resistances and capacitances
Resistances of HTS tapes are obtained by modelling the 𝐶𝑡𝑎𝑝𝑒 (𝑇) = 𝐿 𝑆𝑡𝑎𝑝𝑒 𝛾𝑡𝑎𝑝𝑒 𝑐𝑡𝑎𝑝𝑒 (𝑇) (8)
superconductor by means of the well-known E-J power law,
here stated in its inverse form: where the mass density of the tape is defined as

𝐽𝑐 (𝑇) 𝐸 𝑛−1
1 γ𝑡𝑎𝑝𝑒 = 𝑓𝑓𝐶𝑢 γ𝐶𝑢 + 𝑓𝑓𝐴𝑔 γ𝐴𝑔 + 𝑓𝑓𝐻𝑇𝑆 γ𝐻𝑇𝑆 + 𝑓𝑓𝐻𝑎𝑠𝑡 γ𝐻𝑎𝑠𝑡 (9)
𝐽(𝐸, 𝑇) = ( ) 𝐸 [A/m2] (3)
𝐸𝑐 𝐸𝑐
where Cu, Ag, HTS, Hast represent are mass densities of copper,
The following equivalent voltage- and temperature- silver, superconductor and Hastelloy.
dependant conductivity is defined based on Eq. (3) Moreover, the specific heat of the tape is computed as:

1
−1
𝑐𝑡𝑎𝑝𝑒 (𝑇) =
𝐽𝑐 (𝑇) 𝑉 𝑛
σ𝐻𝑇𝑆 (𝑉, 𝑇) = ( ) + σ𝑛𝑠 (𝑇) [S/m] (4) 𝑓𝑓𝐶𝑢 𝛿𝐶𝑢 𝑐𝐶𝑢 +𝑓𝑓𝐴𝑔 𝛿𝐴𝑔 𝑐𝐴𝑔 +𝑓𝑓𝐻𝑇𝑆 𝛿𝐻𝑇𝑆 𝑐𝐻𝑇𝑆 +𝑓𝑓𝐻𝑎𝑠𝑡 𝛿𝐻𝑎𝑠𝑡 𝑐𝐻𝑎𝑠𝑡
(10)
𝐸𝑐 𝐿⋅𝐸𝑐
γ𝑡𝑎𝑝𝑒

where the electric field E can be substituted with the ratio V/L
and σ𝑛𝑠 (𝑇) is the normal state conductivity to which the power where cCu, cAg, cHTS, cHast are the temperature-dependent specific
law must be smoothly connected during the transition [15],[16]. heats of the tape layers. It is pointed out that the adiabatic model
Based on the equivalent conductivity of the whole tape, defined represents a conservative assumption in terms of possible
in Eq. (5), a temperature- and voltage- dependent resistance can overtemperature that can arise in the cable during transient.
be obtained for the HTS tape as in Eq. (6). However, heat exchange with the coolant and between the
layers of the cable can be included in the model by adding
σ𝑒𝑞 (𝑇) = σ𝐶𝑢 (𝑇)𝑓𝑓𝐶𝑢 + σ𝐴𝑔 (𝑇)𝑓𝑓𝐴𝑔 + transverse thermal conductances [17].
(5)
+σ𝐻𝑇𝑆 (𝑇)𝑓𝑓𝐻𝑇𝑆 + σ𝐻𝑎𝑠𝑡 (𝑇)𝑓𝑓𝐻𝑎𝑠𝑡
D. Reduced equivalent circuit.
1 𝐿 The equivalent circuit depicted in Fig. 4 comprises numerous
𝑅(𝑉, 𝑇) = (6)
𝑆𝑡𝑎𝑝𝑒 σ𝑒𝑞 (𝑇) branches, making it impractical for implementation in power
system simulators. To make it suitable for integration into an
Electro-Magnetic Transient modelling tool, a reduction
where Stape is the cross-section of the tape, Cu, Ag, HTS, Hast procedure is applied to simplify its complexity, in conjunction
are the conductivities and ffCu, ffAg, ffHTS, ffHast are the filling with the model of the hosting DC system. The reduction
factors of copper, silver, superconductor and Hastelloy within procedure assumes that all conductors of the same cable layer
the tape. All other cable conductors (wires or tapes composing (former, HTS layers, shield and pipes) carry the same current
the former and the shield and straight conductors modelling the and operate at the same temperature. Therefore, resistive
metallic pipes) are represented by considering temperature- voltage drop is the same for all conductors of the same layer.
dependent conductance using lookup tables. Capacitance of the Based on this assumption, all conductors of one layer can be
equivalent circuit of Fig. 4, are calculated by means of the merged into one unique conductor whereby the current follows
cylindrical capacitor formula. Capacitances are not considered a helical path, and the reduced cable model schematized in Fig.
between the HTS layers and between the former and HTS1 as 6 is finally obtained. The corresponding equivalent thermal
no insulating medium is included in between. network is shown in Fig. 7.
Resistances, thermal capacitances and heat source terms of
C. Thermal network the reduced equivalent circuit of an individual layer are
The temperatures of all conductors of the cable, required for obtained from the parallel of the individual conductors
the definition of the resistances of the electric circuit, are belonging to the same layer. Based on magnetic conservation
calculated by means of the thermal network shown in Fig. 4b. arguments or, equivalently, by equivalence of the overall circuit
This is obtained by imposing an independent adiabatic thermal behaviour, the inductance coefficients of the reduced equivalent
balance for each of the conductors in the form: circuit are given by:
𝑑𝑇 𝑉2
𝐶𝑒𝑞 (𝑇) = (7)
𝑑𝑡 𝑅(𝑇,𝑉)
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an ideal DC source, therefore, using its actual model including
its control and internal protection algorithm allows the
computation of the real transient current when the fault occurs.
As the fault is located at 100 km from the onshore converter,
the total inductance seen from the converter is very high,
limiting the cable fault current to a low value. Also, as the initial
power flow is from the left to the right of the circuit (the power
is transferred from the wind park to the onshore converter
station), and the AC grid feeds the fault through the converter
Fig. 6. Reduced model and current paths of the HTS power cable.
station, the fault current flows in opposite direction to the steady
state flow direction. Finally, because of the tripping of the
onshore DC CBs, located on the DC side of the Onshore
converter (Fig. 1), the cable current is interrupted after a few
ms. As a result, the fault current starts from the steady state
current of 10 kA and goes smoothly to zero without overshoot,
this is shown in Fig. 8. In the example shown the fault is
initiated at time 0,8 s, when the system is operating in normal
condition transporting the rated current of 10 kA.

a) b)

Fig. 7. Reduced equivalent circuits of the HTS power cable. (a) Electric Circuit
and (b) Thermal Network.

1 Fig. 8. Cable current during offshore DC busbar pole to pole fault.

𝑀𝐴𝐵 = 𝑛 ∑𝑛𝑖=1
𝐴
∑𝑛𝑗=1
𝐵
𝑚𝑖𝑗 (11)
𝐴 𝑛𝐵
Using the implemented cable model, it is possible to evaluate
where MAB is the self/mutual inductance coefficient between the currents in each cable layer (Fig. 9) and their corresponding
two generic layers, nA and nB are the number of elements in temperature rises (Fig. 10). The following results can be
layer A and B respectively, and mij is the generic element of the highlighted:
complete inductance matrix of the cable. The reduced a) Although the total fault current duration is in the order of 15
equivalent circuit consists of eight branches in total, ms, current remains in the different layers, creating internal
corresponding to former, four HTS layer, shield and the two loops with low resistive loss for approximatively 500 ms.
pipes respectively. It is worth noting that all parameters of the b) After the cable current is cleared, there remains magnetic
equivalent circuit are rigorously derived from the inherent energy in the different layers that will dissipate in durations
physical properties of the material composing the conductor, related to layer series resistances and direct inductance
such as electrical resistivity and specific heat capacity, both considering also mutual inductances that will still dictate
temperature-dependent. This approach eliminates the necessity current repartition before reaching a new steady state i.e. no
for making ad-hoc assumptions. current in any of the parallel branches.
c) During the fault, there is an uneven current sharing between
the HTS layers. This distribution is driven by the mutual
IV. RESULTS inductances.
To illustrate the implementation of the SC cable model into d) The copper former is parallel to the HTS layers with no
the full network model, the case of a pole-to-pole fault between coupling capacitance. In contrary, the copper shield is parallel
the positive and the negative DC busbar of the wind-park side to the HTS layers but with coupling capacitances and
(labelled respectively as BB_Offsh_P and BB_Offsh_N in Fig. grounding at its two extremities. It results in a current flow in
2) is considered. For the illustration, the HTS cable is the copper former in the same direction as the cable current
implemented into the ±50 kVdc system. The SC cable length is and, contrary, a current flow in the copper shield in the
100 km, the two SC cable poles are adjacent. All the opposite direction to the cable current.
components of the grid are modelled including the onshore e) HTS4 layer current flows in the opposite direction to the cable
converter as depicted in Fig. 1, that is described using the current and the copper shield current.
average arm model method [18]. The AC/DC converter is not
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f) In HTS2 layer, the current reaches a peak value of 4 kA, implemented into the full 1 GW offshore windfarm export
briefly exceeding its critical current of 3000 A. electrical system where the onshore converter is described as a
g) The most stressed layers in terms of current peak and duration real component using the average arm model and RSFCL as
are the former and the shield. well as DC circuit breakers are modelled. One fault case is
simulated, and its results are discussed. It illustrates how the
The copper former and shield are subjected to a relatively high cable interacts with the full electrical system and how the cable
current and extended current duration, which might lead to internal behaviour can be evaluated in case of a transient current
overheating. However, as depicted in the temperature plot event. Based on these results, the SCARLET project will
shown in Fig. 10, the temperature rise of the shield is not proceed with a simulation plan that encompasses both HTS and
significant, and the temperature increase in the HTS layers is on MgB2 cable cases in order to properly design the protection
the order of 0.1 K, thus not affecting the cable's integrity. devices, including the RSFCL as well as the cables themselves.

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[3] C. E. Bruzek et al., "MgB2-Based MVDC Superconducting Power Cable
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Fig. 10. Temperature distribution in the cable conductive layers.
[12]A. Alefragkis et al., “Next Generation Offshore Grid Connection Systems:
TenneT’s 2 GW Standard,” ELECTRA n° 321, Apr. 2022. [Online].
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appears to be non-critical in terms of current peak and current [13]W. Grieshaber et al., “Adjustable Active Current Injection DC circuit
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duration, the response of each individual layer is not so obvious. [14]F. W. Grover, “Inductance Calculations: Working Formulas and Tables,”
The investigation of each individual current and temperature is Instrument Society of America, Reprinted by permission of Dover
required to ensure there is no risk for the cable safety. It is also Publications, Inc., 1946 and 1973, ISBN: 0-87664-557-0.
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HVDC Transmission Systems”, IEEE Trans. On Power Delivery, Vol. 28,
n. 3, pp. 1723 - 1730, Jul. 2013
V. CONCLUSION
In this paper, a methodology for modelling the equivalent
electrical circuit of superconducting cables is presented. This
cable model, applied to the ±50 kVdc HTS cable, is