Per-Unit Sequence Models

In an ideal Y-Y transformer grounded via neutral impedances, balanced positive or negative-sequence currents flow without producing neutral currents or voltage drops. The per-unit sequence networks resemble those of a single-phase transformer. This symmetry simplifies analysis because positive and negative-sequence impedances are identical, allowing straightforward modeling of balanced fault conditions.

Zero-sequence currents cannot flow to ground through an ungrounded neutral but can still circulate within the windings. These identical-magnitude, in-phase currents combine to form a neutral current, causing voltage drops across the neutral impedance and affecting the low-voltage winding voltage. This circulation path allows zero-sequence analysis even without a ground connection.

Practical Y-Y transformers incorporate external impedances in their per-unit sequence networks. Shunt branches represent balanced-Y impedance loads, with each phase containing a core loss resistor in parallel with magnetizing inductance. Despite these additions, positive and negative-sequence impedances remain identical, while zero-sequence networks depend on neutral impedance configuration.

Delta-delta transformers have identical positive and negative-sequence networks with per-unit impedances independent of winding connections. This consistency simplifies fault analysis since both sequence types experience the same impedance. However, practical transformers may show variations depending on actual winding configuration and core design.

Three-phase, three-winding transformers are modeled by connecting three identical single-phase transformers using a common S-base for all terminals and proportional voltage bases for each winding. This approach ensures consistent per-unit representation across all three phases and windings, enabling accurate analysis of sequence currents and voltages throughout the transformer.

In the general zero-sequence network, the high-voltage winding configuration dictates the high-voltage connection and determines how zero-sequence currents flow through the transformer. Different configurations—such as grounded or ungrounded Y, or delta—create different zero-sequence paths and impedances, directly affecting fault current distribution and voltage response during unsymmetrical faults.

Per-unit sequence models decompose unsymmetrical faults into positive, negative, and zero-sequence components, each with defined impedances. By analyzing how sequence networks of rotating machines and transformers interact during faults, engineers can calculate fault currents and voltages. This approach enables proper circuit breaker and fuse selection for system protection.