Carloni Paper
Carloni Paper
Carloni Paper
The article describes the analysis of the electric and thermal impact of HVDC electrode installations, which use
the earth and/or sea as the conductive medium for the HVDC transmission system.
The analysis requires the modeling of both local and remote impacts, using multiple coupled 2D/3D models in
the AC/DC module, each describing the physics of the HVDC link at different scales: 2D electric current
coupled to lumped parameter circuits physics for evaluation of corrosion on metal structures such as pipes or
railways in the large scale models, 3D models with electric currents, joule heating and convective heating
physics for evaluation of voltages and temperature in the models of the electrodes.
The results of the analysis can be used highlight potential health hazards (or lack thereof), and to define
mitigation measures, test specifications and maintenance intervals.
Figure 5 – Depletion rates along a pipeline length, based Electrode resistance to remote earth, thermal heating
upon the assessment of the stray currents. effects and electro-osmotic effects are dependent on
the design of the electrode. A large electrode with
Local electric effects
large contact surface to the host material is less likely
For sea electrodes, it is important to keep electric fields
to have problems but will also be more expensive.
low to avoid effects on swimmers accidentally
A proper selection of electrode site might therefore be
entering the area and sea animals. The current density
cost saving.
must also be kept low to avoid unacceptably high
chlorine emissions.
The evaluation of the electric field strength around
The low resistivity of salty or brackish water will
submerged coastal electrodes, and the current density
usually keep electric fields at low levels around sea
at the electrode are used, among other things, to
and shore electrodes but significant electric fields can
determine the impact in terms of electrolysis products
occur if a sea electrode is located in a shallow water
from the anode, such as hypochlorite, hypobromite,
environment underlain by high-resistivity solid,
bromide, chloroform and bromoform.
crystalline rock. The seawater will almost act as one
Further concerns are economical, to determine
single large electrode volume in such cases and high
material selection (typically titanium mesh), electrode
electric gradients can be created perpendicular to the
testing and commissioning.
shoreline at quite large distances from the electrode. It
is therefore important to select sites with rapid
Other applications are temperature rise evaluations
transition to deep water and direct access to the open
(for land electrodes).
sea.
The temperature at any point of the soil can be
determined by solving the Laplace differential
Figure 6 shows a 3D model of the voltage equation of heat conduction
distribution in a 1kmx1km area around three sea
electrodes which was used to determine touch ∇(𝑘 𝑇 ∙ ∇𝑇) + 𝑔 = 𝑑𝑠 ∙ 𝛾 ∙𝜕𝑇𝑖,𝑗,𝑙.
voltages.
Similar models can be used for land electrodes to
With 𝑔 = 𝜌 ∙ 𝐽2 , and where
determine touch and step voltages, to determine
transferred potentials along long metallic fences and
Figure 7 – Electrode design prior to optimization. High A similar feature can be exploited to couple 2D models
current density at the corners of the electrode may cause of the area with more detailed 3D models of the
release of chlorine gas. electrode arrangements.
Figure 9 shows an area in the 2D model 1 with higher
depth and resistivity resolution. The edges of the
Coupling large scale models to local models higher resolution areas are defined are generally
The electric voltage, current and temperature extruded (in mod1>Definitions, apply genext1 to the
distributions for the HVDC link can be evaluated boundaries). Then the voltages are mapped, by
using multiple coupled 2D/3D models in the AC/DC applying the mod1.genext1(V) in the 3D model 2, in
module of COMSOL5.4, each describing the physics the physics node, electric currents, electric potential.
of the HVDC link at different scales.
For the evaluation of the voltage distributions along
the entire length of the HVDC link one may use a 2D
models of the area surrounding the installation such as
the one shown in Figure 1, describing the topography
(bathimetry) of the region and resistivity of the
soil/water (in the case of subsea electrodes), in which
the anode and cathode are represented by electric
current point sources, and pipes and metal structures
can be represented by external lumped parameter
circuits, coupled to physical points in the model via Figure 9 – The general extrusion feature is used to map
voltage coupling. voltage distributions along the highlighted edges of the 2D
The sea depth function z(x,y) and the corresponding model to the corresponding boundaries in the 3D model.
resistivity function sigma(x,y) are imported as simple
interpolation functions and applied as material
properties.
In order to have a better resolution around the sources, Coupling electric currents and lumped
the large scale 2D model (model 1) is then coupled to circuits
smaller scale 2D models (model 2) of the area Pipelines, metal fences and transmission lines can be
surrounding the electrodes, using the general extrusion represented as lumped parameter circuits, with a given
feature to map the voltage distributions found in the resistance along the pipe and resistance to soil (or
larger models to the boundaries of the smaller model. water), which exchange voltage and current with the
Figure 8 shows areas in the model 1 with higher depth 2D FEM model.
and resistivity resolution. The edges of the higher Long lines of point-like terminals in the 2D FEM
resolution areas are defined are identity mapping (in model, represent the pipe segmented into fixed length
mod1>Definitions, apply idmap1 to the boundaries). sections. Each terminal exchanges current with the
Then the voltages are mapped, by applying the corresponding lumped parameter circuit section
External I Vs. U 1.
References
Conclusions
The complexity of the evaluations involved for the
feasibility studies for HVDC links discussed above,
requires the use of finite element models.
Ground potential rise, potential gradient and
maximum step/touch voltage, and DC resistance to
remote earth can be mathematically estimated for
various types and shapes of electrodes for the soil
resistivity of uniform, 2-layer or 3-layer distribution.
However, such methods are not sufficient if the soil in
the immediate area of the electrode is not of uniform
resistivity or when operation is required with outages
of a portion of the electrode.
Similarly, estimates of the average current density
from an electrode would fail to capture the high
current density from sharp corners or to provide mush
input into the electrode design optimization.
For these evaluations FEM simulations are required.
Furthermore, the evaluations, though generally based