Lesson 4 of 8

Transformers

8 min read

The transformer is arguably the single piece of equipment that makes the modern power system possible — it's what let engineers separate "the voltage that's efficient to transmit" from "the voltage that's safe to use," a problem the very first lesson in this track raised without yet explaining how it's solved. This lesson explains the device itself, before the next lesson (the per-unit system) shows how it can be made to mathematically disappear from calculations.

The basic principle: mutual induction

A transformer has no moving parts and no direct electrical connection between its two sides. Two coils of wire are wound around a shared magnetic core; an alternating current in the first (primary) winding creates a changing magnetic flux in the core, and that changing flux induces a voltage in the second (secondary) winding purely through electromagnetic induction. The ratio between the two voltages is set entirely by the ratio of the number of turns in each winding:

V₁V₂ = N₁N₂ = I₂I₁

Ideal transformer relationship

Notice current is inversely proportional to the turns ratio, unlike voltage — an ideal transformer transfers power (V × I) unchanged from one side to the other, it just trades voltage for current, or current for voltage, in a fixed ratio.

Why a real transformer isn't quite ideal

Real transformers depart from the ideal relationship above in a few well-understood ways, commonly represented together as an equivalent circuit: winding resistance causes I²R (copper) losses; not all magnetic flux links both windings, creating leakage reactance; and the core itself consumes some power magnetizing and re-magnetizing every cycle, causing core (iron) losses. For most system-level studies, these effects are lumped into a single equivalent series impedance — which is exactly the transformer impedance you convert to per-unit in the next lesson.

Three-phase transformer connections

A three-phase transformer bank connects its primary and secondary windings using the same star (Y) and delta (Δ) options covered in the three-phase power lesson — and the choice on each side matters a great deal:

Yy: Star on both sides. Provides a neutral on both windings, but offers no path for third-harmonic circulating current, which can be a drawback without additional design measures.
Dy (or Yd): Delta on one side, star on the other — extremely common for distribution transformers, since it provides a neutral on the star side (for line-to-neutral loads) while the delta side gives a natural path for third-harmonic currents to circulate.
Dd: Delta on both sides. No neutral on either side, but robust against certain unbalanced conditions — common in some transmission-level applications.

The phase shift you can't ignore

Any connection mixing star and delta (Dy or Yd) introduces a fixed phase shift — commonly 30° — between primary and secondary line voltages. This isn't a flaw; it's a direct geometric consequence of the winding connection. It becomes critically important the moment you try to connect transformers in parallel, since mismatched phase shifts between units would otherwise drive large circulating currents between them.

Autotransformers, briefly

An autotransformer uses a single winding, tapped at an intermediate point, instead of two electrically separate windings — cheaper and more efficient for applications with a relatively small ratio between primary and secondary voltage, at the cost of a direct electrical connection between the two sides (losing the electrical isolation a two-winding transformer provides). Common in transmission systems connecting two relatively similar high voltage levels.

Instrument transformers: CTs and VTs

A separate, smaller class of transformer exists purely to make measurement and protection possible: instrument transformers scale dangerous, hard-to-measure primary quantities down to small, standardized, safe values for relays and meters — without instrument transformers, every meter and protection relay would need to be built to withstand full system voltage and current directly.

Current Transformer (CT): Scales a large primary current down to a small standardized secondary current (commonly 1 A or 5 A), for protection relays and metering. Connected in series with the circuit being measured.
Voltage Transformer (VT / PT): Scales high primary voltage down to a small standardized secondary voltage (commonly 100 V or 110 V), for the same purpose. Connected in parallel across the circuit being measured.

The classic CT safety rule

A current transformer's secondary must never be left open-circuited while primary current is flowing. Because a CT is fundamentally a current source on its secondary side, an open circuit forces the full primary ampere-turns into magnetizing the core with nowhere else to go, producing a dangerously high secondary voltage spike — a well-known hazard, and exactly why CT secondary circuits are always short-circuited before any relay or meter connected to them is disconnected for maintenance.

Key takeaways

A transformer transfers power between windings via mutual induction, trading voltage for current according to the turns ratio.
Real transformers have resistance, leakage reactance and core losses, usually lumped into a single equivalent series impedance.
Three-phase connections (Yy, Dy, Dd) each have different neutral and phase-shift implications — Dy is the most common for distribution.
Instrument transformers (CTs and VTs) scale voltage and current down safely for protection and metering — never open-circuit a CT secondary under load.