Equivalent circuits; transformer on dc supply

Equivalent circuit referred to primary or secondary

A real transformer has winding resistances R1, R2, leakage reactances X1, X2, and a no-load branch (Ro, Xo). To solve it as a single-voltage circuit, all quantities are expressed on one side, with K = N2/N1.

Rules for transferring impedance from one side to the other

• Voltage, current and impedance transform as: V2′ = V2/K, I2′ = K I2, Z2′ = Z2/K² (secondary to primary).
• The reverse: Z1′ = K² Z1 (primary to secondary).
• The VA, power and losses stay the same, only the base voltage changes.

The magnetising branch is usually moved to the input terminals (approximate circuit), since the no-load current is small.

 I1     R01      X01         I2'
 o──┬───/\/\/──────(((────────────o
    │                           
   Ro∥Xo                    load, V2'
    │                           
 o──┴─────────────────────────────o
   (referred to primary; reverse for secondary)

Referring to the secondary uses R02, X02, and the shunt branch Ro′, Xo′ at the output side in the same way.

Transformer connected to a d.c. supply of the same voltage rating

• A transformer works only on a changing flux. A d.c. supply creates a constant flux, so no back emf (E1 = −N dΦ/dt = 0) is induced in the primary.
• The only opposition to the current is the very low winding resistance R1. The current is I = V/R1, which is many times (often 20 to 100 times) the rated current.
• The large current heats the winding (I²R) and the insulation, and the primary winding burns out unless a fuse or circuit breaker acts quickly.
• The core may also saturate. A transformer must never be connected to d.c.