Overview

In high-voltage power system design, laboratory measurements and field tests are often considered the gold standard. However, these approaches have inherent limitations: physical space constraints, high costs, and the inability to directly measure certain phenomena under real-world conditions. Modern simulation techniques overcome these hurdles by accelerating design, reducing costs, and enabling assessment of scenarios that are impractical to test physically. This tutorial explores two industry examples where simulation provides critical insights. First, we examine corona performance testing of high-voltage transmission line hardware, particularly for 500 kV and 765 kV systems. Second, we investigate induced electric fields around HVDC submarine cables—a subtle effect caused by ocean currents moving through static magnetic fields. By the end of this guide, you will understand how to translate single-phase laboratory corona tests into accurate three-phase predictions and how to model electromagnetic phenomena that are often overlooked.

Prerequisites

To follow this tutorial, you should have:

• Basic understanding of high-voltage engineering concepts (e.g., corona discharge, electric field strength)
• Familiarity with electromagnetic theory, especially Faraday’s law of induction
• Knowledge of simulation tools (e.g., COMSOL Multiphysics, ANSYS Maxwell, or similar finite element method software)
• Access to a computer with simulation software installed (trial versions are sufficient)
• Optional: Background in power system design for transmission lines and submarine cables

Step-by-Step Instructions

Case 1: Simulating Corona Performance of Transmission Hardware

Corona-free performance of insulator hardware is essential for reliable operation at voltages ≥500 kV. Laboratory mockups are typically limited to partial single-phase setups due to space constraints. The challenge is establishing equivalence between the lab single-phase test and real-world three-phase conditions. Simulation solves this by modeling the full three-phase environment. Follow these steps:

1. Define the Geometry – Create a 3D model of the transmission line hardware including insulators, conductor bundles, and fittings. Use exact dimensional data from the physical components.
2. Set Material Properties – Assign electrical conductivity and permittivity for metals, insulators, and air. For corona prediction, focus on air’s dielectric breakdown strength (~3 kV/mm under standard conditions).
3. Apply Boundary Conditions – In the single-phase lab setup, apply a sinusoidal voltage (e.g., phase-to-ground) to the energized component. Model the ground plane and shield walls as perfect conductors at zero potential. For the three-phase equivalent, apply three voltage sources with 120° phase shift.
4. Define Mesh – Use a fine mesh in regions of high electric field gradient, such as edges of conductor fittings. An adaptive mesh can refine during solution.
5. Solve the Electrostatic Field – Use a finite element solver to compute the electric field distribution. Identify regions where the field exceeds the corona inception threshold (typically 20–30 kV/cm for clean surfaces).
6. Validate Equivalence – Compare the maximum field strength and corona onset voltage between the single-phase lab model and the three-phase model. Adjust the lab setup parameters (e.g., voltage level, spacing) in simulation until the field patterns match. This yields a correction factor for translating lab results to real-world conditions.
7. Iterate Design – Use simulation to test hardware modifications (e.g., adding corona rings) without building multiple physical prototypes.

Case 2: Simulating Induced Electric Fields from HVDC Submarine Cables

HVDC submarine cables for offshore wind interconnects are often considered environmentally inert because the internal electric field is contained and static magnetic fields do not induce voltages in stationary objects. However, ocean currents flowing through the static magnetic field create relative motion, satisfying Faraday’s law and inducing external electric fields. These fields, though weak, are detectable by aquatic species like sharks and rays. Simulation is essential because direct measurement in the ocean is challenging. Proceed as follows:

1. Build the Cable Model – Create a 2D or 3D geometry of the submarine cable cross-section, including conductor, insulation, sheath, armoring, and any external layers. For simplicity, assume a long straight cable.
2. Define Material Properties – Assign electrical conductivity (σ) and magnetic permeability (μ) for copper conductor, XLPE insulation, steel armor, and seawater (σ ≈ 4 S/m). Note that seawater is conductive, so induced currents can flow.
3. Set Source Current – Apply a constant DC current (e.g., 2000 A) to the conductor. This generates a static magnetic field (B) that encircles the cable according to Ampère’s law.
4. Model Ocean Current – Introduce a uniform flow velocity (v) perpendicular to the cable axis (e.g., 1 m/s). This is the relative motion between the seawater and the magnetic field.
5. Apply Faraday’s Law – In simulation, use the MHD (magnetohydrodynamic) module or a customized formulation to compute the induced electric field (E) from E = v × B. Ensure the solver accounts for the conductive medium.
6. Solve for Electric Potential – Since the induced fields are conservative? Actually, due to the conductive seawater, the induced currents redistribute charge, leading to an electric potential that can be computed via Poisson’s equation. Set boundary conditions at the cable outer surface (insulation) and far-field (zero potential at large distance).
7. Analyze Results – Plot the external electric field magnitude around the cable. Typical values range from microvolts per meter to millivolts per meter, depending on cable load and current velocity. Compare with detection thresholds of marine animals (e.g., 1–10 μV/m for some sharks).
8. Sensitivity Studies – Vary parameters like cable burial depth, ocean current speed, and conductor current to assess environmental impact.

Common Mistakes

• Assuming lab single-phase tests directly represent three-phase reality – Without simulation, the equivalence factor is often guessed, leading to corona issues in the field. Always use a validated numerical model.
• Neglecting relative motion in static magnetic fields – Many engineers think HVDC cables are completely inert outside. Ocean currents create induced fields; ignoring this can lead to environmental oversight.
• Overly coarse meshing – In corona simulation, sharp edges require fine mesh for accurate field gradients. Coarse meshing underestimates peak fields.
• Using wrong material properties – For submarine cables, seawater conductivity varies with temperature and salinity; use realistic values rather than pure water.
• Forgetting the insulation boundary – In the cable model, the external electric field is only induced in the seawater; the cable’s insulation shields the internal field. Ensure proper boundary conditions.

Summary

This tutorial demonstrated how simulation overcomes the limitations of physical measurements for two critical power system problems: corona performance of high-voltage transmission hardware and induced electric fields from HVDC submarine cables. By following the step-by-step instructions—from geometry setup to field solution—you can accurately translate single-phase lab tests to three-phase real-world performance, and model subtle electromagnetic interactions with ocean currents. The key takeaway is that modern simulation reduces design costs, speeds up development, and reveals phenomena that are otherwise unmeasurable. Apply these techniques to your next high-voltage project to improve reliability and environmental understanding.