Insulation-Structure Optimization for a Uniform Air Field and Optimal Gas-Mixture Selection for 500 kV Eco-Friendly Gas-Insulated Current Transformers

Technical Summary: Insulation-Structure Optimization and Gas-Mixture Selection for 500 kV Eco-Friendly Gas-Insulated Current Transformers

Problem Statement
The transition to ultra-high-voltage (UHV) substations requires current transformers (CTs) that balance high dielectric strength with environmental sustainability. Conventional oil-immersed and epoxy-resin CTs face risks of fire, aging, and failure under harsh conditions, while SF6-insulated CTs, despite their superior dielectric properties, possess a high global warming potential (GWP) of 23,500, conflicting with the Paris Agreement and China's "dual-carbon" goals. Replacing SF6 with eco-friendly alternatives like clean dry air or N2/O2/He mixtures presents a significant engineering challenge: these gases exhibit dielectric strengths roughly 30–35% lower than SF6 at equivalent pressures. Consequently, engineering air-type CTs requires overcoming non-uniform electric fields, managing the trade-offs between dielectric strength, thermal diffusion, detection sensitivity, environmental impact, and cost, and ensuring robustness against manufacturing tolerances and operating fluctuations. Existing research lacks a systematic approach for 500 kV eco-friendly gas CTs that simultaneously optimizes geometry, gas composition, and operating parameters while accounting for real-world uncertainties.

Methodology
The paper proposes a closed-loop design framework integrating geometric dimension reduction, multi-objective gas optimization, and robustness screening.

1. Global Sensitivity Analysis for Geometric Reduction:
   To address the high dimensionality of the design space (seven geometric variables), a three-stage screening process was employed:

   • Morris Screening: Used to identify parameters with significant main effects and interactions.
   • Kriging Surrogate Modeling: A Gaussian process surrogate was trained on Latin hypercube sampling data to approximate the maximum electric field strength ($E_{max}$) and field-distortion coefficient ($k_E$), achieving a cross-validation $R^2 \geq 0.95$.
   • Sobol Variance Decomposition: Applied to the surrogate model to quantify first-order and total-effect indices, revealing interaction contributions.
     This process reduced the geometric design space from seven variables to four key parameters: high-voltage electrode fillet radius ($r_{hv}$), intermediate-electrode normalized position ($h_m$), intermediate-electrode length ($l_m$), and main insulation gap ($d$).

2. Multi-Objective Pareto Optimization (NSGA-II):
   A Non-dominated Sorting Genetic Algorithm II (NSGA-II) was utilized to optimize the N2/O2/He gas mixture ratios and absolute pressure. The optimization targeted five conflicting objectives:

   • Dielectric performance (breakdown, PD, and impulse margins).
   • Thermal diffusion (thermal conductivity and temperature-rise margin).
   • Detection sensitivity (fault gas response and He tracer retention).
   • Environmental impact (GWP and toxicity).
   • Engineering cost (gas, sealing, and manufacturing costs).
     The electric field quantities required for the objective functions were predicted in real-time by the Kriging surrogate, avoiding repeated finite-element simulations.

3. Robustness Assessment:
   To ensure engineering applicability, 1,000 Monte Carlo simulations were performed for each Pareto-optimal solution. These simulations accounted for uncertainties in geometric manufacturing tolerances ($\pm 0.5$–$2$ mm), gas pressure fluctuations ($\pm 5\%$), ambient temperature variations ($-40^\circ\text{C}$ to $+60^\circ\text{C}$), and gas-mixture filling accuracy. Solutions were filtered based on a robustness index ($\eta = \mu/\sigma$) and a 5% quantile constraint for the electric-field safety margin ($P_{5}M_E \geq 1.2$).

4. Comprehensive Evaluation and Weighting:
   To select a single recommended scheme from the Pareto front, the paper combined subjective Analytic Hierarchy Process (AHP) weights with objective Entropy weights. The consistency of the resulting rankings was verified using Spearman rank-correlation coefficients.

Key Contributions

• Dimensionality Reduction: The study quantitatively demonstrated that the high-voltage electrode fillet radius ($r_{hv}$) and intermediate-electrode position ($h_m$) are the dominant factors influencing $E_{max}$, accounting for nearly 88% of the output variance. This allows for a focused optimization strategy rather than a computationally expensive full-factorial scan.
• Integrated Optimization Framework: The paper establishes a method that couples structural geometry optimization with gas-mixture selection, moving beyond single-factor empirical approaches.
• Robust Design Strategy: By superimposing Monte Carlo robustness assessments on the Pareto front, the study identifies solutions that maintain safety margins under realistic operating disturbances, addressing a gap in deterministic optimization studies.
• Weighting Consistency: The combination of AHP and Entropy methods, validated by high Spearman correlation ($\rho > 0.85$), provides a stable and defensible basis for ranking multi-objective solutions in engineering design.

Results
For the 500 kV case study, the recommended configuration is:

• Geometry: $r_{hv} = 45$ mm, $h_m = 0.52$.
• Gas Mixture: $\alpha_{N2} = 0.78$, $\alpha_{O2} = 0.21$, $\alpha_{He} = 0.01$ (1% volume fraction).
• Pressure: $p = 0.5$ MPa.

Performance Comparison:

• The recommended scheme achieved a composite score ($J$) of 0.812.
• It outperformed the SF6 baseline by 17% (driven primarily by environmental score improvements).
• It exceeded the dry-air scheme by 14% (due to better dielectric and thermal performance).
• It surpassed the N2/CO2 scheme by 17%.
• Robustness: The recommended scheme demonstrated a robustness index $\eta = 17.5$ for the electric-field safety margin, with $M_E \geq 1.74$ in 95% of operating conditions. This is superior to the no-He scheme ($\eta = 11.4$) and the high-He scheme ($\eta = 10.7$), though lower than the inherent robustness of SF6 ($\eta = 28.9$).

Significance and Claims
The paper claims that this methodology provides a quantitative basis for the forward design and prototype verification of eco-friendly UHV current transformers. By shifting gas-mixture selection from empirical settings to a constrained robust optimization output, the approach addresses the critical trade-offs between insulation reliability, environmental impact, and cost. The authors assert that the proposed framework is stable and can be embedded into future digital-twin models. The study concludes that a trace amount of Helium (~1%) is sufficient for leak-tracing detection without incurring the high costs associated with higher concentrations, while the optimized geometry and gas pressure compensate for the lower dielectric strength of eco-friendly gases compared to SF6. Future work is suggested to involve Physics-Informed Neural Networks (PINN) for faster field prediction and experimental validation of prototype partial discharge data.