Statistical approach to non-invasive modeling of zigzag transformers using variable impedance

Zigzag transformers are essential components in modern power systems for grounding, neutral point establishment, and harmonic filtering in FACTS devices, smart grids, and arc suppression systems. These transformers exhibit highly nonlinear behavior with core saturation and hysteresis effects, present significant challenges for accurate modeling in modern power system analysis. The practical engineering challenge of developing reliable models without access to proprietary internal parameters represents a critical gap in power system analysis, creating significant modeling challenges when internal parameters remain inaccessible due to operational constraints, safety requirements, and intellectual property limitations. This paper introduces a statistical, non-invasive methodology for modeling zigzag transformers using variable impedance derived from external testing procedures including DC resistance measurements, three-phase no-load tests, and single-phase open-circuit tests—all conducted without internal access requirements. Advanced polynomial curve-fitting techniques with rigorous error analysis create a black-box model capturing variable impedance characteristics across the tested frequency range. The model achieves validated accuracy with correlation coefficients R 2 > 0 . 95 for voltage predictions and R 2 > 0 . 92 for current predictions. Validation through MATLAB Simulink simulations and experimental grid verification demonstrates effective transformer performance prediction under various operating conditions, enabling power system analysis without detailed internal information while enhancing stability and reliability for FACTS devices and arc suppression systems. • Develop a non-invasive statistical methodology for modeling zigzag transformers with uncertainty quantification. • Implement external testing protocols (DC resistance, no-load, single-phase) with numerical sensitivity analysis. • Create a variable impedance black-box model using polynomial curve fitting with error bounds. • Validate the model through MATLAB Simulink simulations with frequency domain analysis and experimental grid verification. • Demonstrate accurate transformer performance prediction under various operating conditions with quantified accuracy metrics.