Understanding Zero-Sequence Impedance and Core Construction in Transformers

The concept of zero-sequence impedance is crucial in the design and analysis of transformer cores. Notably, the zero-sequence impedance for three-phase five-limb constructions is significantly higher than that of three-limb configurations. This difference primarily stems from the low reluctance path offered by yokes and end limbs to in-phase zero-sequence fluxes. When small enough voltages are applied during the zero-sequence test, the impedance value remains close to, yet slightly less than, the positive-sequence impedance. For a deeper dive into zero-sequence impedances across various core designs, interested readers can refer to Chapter 3 of related texts.

The construction of transformer cores involves careful consideration of lamination stacking to minimize losses. When laminations are placed, they are intentionally designed so that gaps at the joints between limbs and yokes are overlapped by subsequent layers. This overlap, typically ranging from 15 to 20 mm, ensures a continuous magnetic path. Different types of joints—such as non-mitered and mitered joints—are employed to further enhance efficiency. Non-mitered joints, with a 90° overlap, are simpler to manufacture but result in higher losses due to improper flux orientation. In contrast, mitered joints, which overlap at angles between 30° and 60° (most commonly 45°), align better with grain orientation, thus reducing losses.

The choice of materials also plays a significant role in transformer efficiency. Higher-grade materials, such as Hi-B and scribed grades, exhibit a specific loss reduction of about 15 to 20% compared to conventional materials. However, merely using superior grades does not guarantee reduced losses unless an appropriate building factor is applied in calculations. This factor, defined as the ratio of loss per weight in the core to the loss per weight in the transformer, increases with the quality of the material. It reflects the increased penalties for deviations in flux direction at joints for better grades.

It’s important to note that the building factor can vary based on the operating flux density, often deteriorating quickly at higher densities. Consequently, while single-phase two-limb transformers may outperform three-phase cores, the building factor for domain-refined grades can even drop below 1.0. This is primarily due to the less congested flux distribution in lightly loaded joints compared to the more crowded conditions in three-phase configurations.

Understanding the implications of core construction and zero-sequence impedance is vital for engineers and designers aiming to optimize transformer performance. Proper calculations and material selections, alongside effective core design techniques, can significantly enhance the efficiency and reliability of transformers in various applications.