An ideal transformer transforms currents in the inverse ratio of the turns in its windings.
From (2.10) and (2.13),
(2.14)
Instantaneous power input to the primary equals the instantaneous power output from the secondary.
Impedance transformation properties: Fig. 2.8.
Figure 2.8 Three circuits which are identical at terminals ab when the transformer is ideal.
(2.15)
(2.16)
(2.17)
(2.18)
(2.19)
Transferring an impedance from one side to the other is called “referring the impedance to the other side.” Impedances transform as the square of the turns ratio.
Summary for the ideal transformer:
Voltages are transformed in the direct ratio of turns.
Currents are transformed in the inverse ratio of turns.
Impedances are transformed in the direct ratio squared.
Power and voltamperes are unchanged.
§2.4 Transformer Reactances and Equivalent Circuits
A more complete model must take into account the effects of winding resistances, leakage fluxes, and finite exciting current due to the finite and nonlinear permeability of the core.
Note that the capacitances of the windings will be neglected.
Method of the equivalent circuit technique is adopted for analysis.
Development of the transformer equivalent circuit
Leakage flux: Fig. 2.9.
Figure 2.9 Schematic view of mutual and leakage fluxes in a transformer.
Two tests serve to determine the parameters of the equivalent circuits of Figs. 2.10 and 2.11.
Short-circuit test and open-circuit test
Short-Circuit Test
The test is used to find the equivalent series impedance
.
The high voltage side is usually taken as the primary to which voltage is applied.
The short circuit is applied to the secondary
Typically an applied voltage on the order of 10 to 15 % or less of the rated value will result in rated current.
See Fig. 2.12.Note that
.
Figure 2.12 Equivalent circuit with short-circuited secondary. (a) Complete equivalent circuit.(b) Cantilever equivalent circuit with the exciting branch at the transformer secondary.