Transformers
Static energy converters built on alternating flux.
Lessons
How EMF is generated
Faraday + Lenz from the ground up: motional EMF, transformer EMF, and the 4.44·f·N·Φ result.
Transformer action under load
Why loading the secondary forces the primary to draw more current.
Transformer phasor diagrams
From no-load through unity, lagging, and leading power factors — the whole steady state in one picture.
Equivalent circuit + OC and SC tests
Two simple lab tests that pin down every parameter of the transformer's equivalent circuit.
Voltage regulation across power factors
Why terminal voltage drops on lagging loads — and actually rises on leading loads.
Three-phase transformer connections + vector groups
Yy0, Dd0, Yd1, Dyn11 — clock-notation phase displacement, paralleling rules, open-delta operation.
Per-unit analysis in transformers
Nameplate %Z, base conversion to system MVA, the single-impedance equivalent, parallel-operation load sharing, auto-transformer kVA saving, and SLG-fault calculation through a Δ-Y_n transformer.
Transformer tap changers — NLTC and OLTC
On-load and off-circuit tap changers, the diverter/selector make-before-break mechanism, ±10 % range in 16 steps, why taps live in the HV winding, and OLTC control with line-drop compensation.
Scott connection — three-phase to two-phase conversion
Two single-phase transformers (main M + teaser T at 86.6 %) convert 3-φ to balanced 2-φ output in quadrature. Geometric derivation, phasor proof, and modern use in single-phase traction substations.
Auto-transformer — savings, tertiary, applications
Single shared winding → S_winding/S_load = (1-1/a). Sweet spot a ≤ 3. Tertiary delta winding for triplen harmonics + neutral stability. Grid 138/230/345 kV ties, motor starters, voltage regulators.
Transformer parallel operation
Essential conditions (V ratio, phase sequence, vector group, polarity). Load divides inversely with Z_pu on common base. Voltage-ratio mismatch → circulating current. ANSI 90 OLTC parallel control.
Three-winding transformers
Three magnetically-coupled windings, three short-circuit impedances (Z_ps, Z_pt, Z_st) → Y-equivalent legs Z_p, Z_s, Z_t. Regulation cross-coupling. GSU + station service application. 87T with 3 CT inputs.