Perfectly Coupled Transformer Figure P15–43 is an equivalent circuit of a perfectly coupled transformer. This model is the basis for the transformer equivalent circuits used in the analysis of power systems.

The inductance Lm is called the magnetizing inductance. The current through this inductance represents the current needed to establish the magnetic field in the transformer at no load ði2ðtÞ ¼ 0Þ. Show that the i–v equations for this circuit are:

v1ðtÞ ¼ Lm di1ðtÞ

dt

þ nLm di2ðtÞ

dt v2ðtÞ ¼ nLm di1ðtÞ

dt

þ n2Lm di2ðtÞ

dt Use these equations to show that k ¼ 1 and v2ðtÞ=v1ðtÞ ¼ n.

Transcribed Image Text:

i1(t) ni2(t) i2(t) 1:n + v1(t) Lm V2(t) Ideal FIGURE P15-43