Admittance matrix models of multi-phase multi-winding transformers

The power transformer is a vital element in the electrical energy distribution and transmission network. It enables efficient and cost-effective power transfer by optimizing voltage levels to reduce current, thereby minimizing power losses across the system. However, transformers can experience operational issues, such as ground faults between the ground and windings or phase-to-phase short circuits. In the event of a fault, a transformer can inflict severe damage on the power grid. Consequently, maintaining optimal transformer conditions remains paramount for stable power grid operation, prompting industry professionals to delve into a comprehensive understanding and rigorous analysis of these essential devices. Meanwhile, understanding the nodal admittance matrix (also referred to simply as the admittance matrix) is important in power system analysis. The nodal admittance matrix is generally designated by the symbol, Y. The general approach is to first build Y from the primitive nodal admittance matrix for each element. A transformer is modeled with a primitive nodal admittance matrix, which is used to build the system Y matrix. The report aims to model and analyze multi-phase, multi-winding transformers using the admittance matrix. Specifically, the modeling focuses on the impact of core effects caused by zero-sequence currents in three-legged core transformers. First, a circuit consisting of a three-winding transformer was modeled using the Y matrix. An analysis of critical parameters, including voltage, current, and power values, was conducted under a normal operating condition. Subsequently, to verify the core effects due to the zero-sequence impedance in the three-winding transformers, a four-winding transformer was modeled and compared with the results of the three-winding transformer under both normal and short-circuit conditions. In conclusion, a modeling solution was proposed to accurately represent the core effects observed in a three-winding transformer.