\[K = \frac{LV}{HV}\]
Transformation Ratio (K):\[(\text{KVA})_{\text{induction}} = (V_1 - V_2)
I_1\]
Inductive Power in Autotransformer:\[\text{I/P KVA} = V_1 I_1\]
Input Power in Autotransformer:\[\frac{(\text{KVA})_{\text{induction}}}{\text{I/P
KVA}} = \frac{(V_1 - V_2) I_1}{V_1 I_1} = 1 - \frac{LV}{HV} = 1 -
K\]
Relationship for Inductive Power:\[(\text{KVA})_{\text{conduction}} = \text{I/P KVA}
- (\text{KVA})_{\text{induction}}\]
Conductive Power in Autotransformer:\[\propto (N_1 -
N_2) I_1\]
Weight of Conductor in Section AB of
Autotransformer:\[\propto (I_2 -
I_1) N_2\]
Weight of Conductor in Section BC of
Autotransformer:\[\propto I_1 (N_1 - N_2) + (I_2 - I_1)
N_2\]
Total Weight of Conductor in Autotransformer:\[\propto I_1 N_1 + I_2
N_2\]
Total Weight of Conductor in Two-Winding
Transformer:\[\frac{\text{wt. of
conductor in an auto t/f}}{\text{wt. of conductor in 2 wdg t/f}} =
\frac{2 (N_1 - N_2) I_1}{2 N_1 I_1} = 1 -
\frac{N_2}{N_1}\]
Weight of Conductor in Autotransformer
(Comparison):\[\text{Wt. of conductor in
auto t/f} = (1 - K) \times (\text{wt. of conductor in 2 wdg
t/f})\]
Weight of Conductor in Autotransformer (Related to
Saving):\[\text{Saving} = K \times \{\text{conductor
wt. in 2 wdg transformer}\}\]
Conductor Material Saving in Autotransformer:\[(\% \text{FL Losses})_{\text{Auto t/f}} =
(1 - K) (\% \text{FL Losses})_{\text{2 wdg t/f}}\]
Full-Load Losses (FL Losses) in Autotransformer:\[(\% Z)_{\text{AT}} = (1 - K) (\% Z)_{\text{2 wdg
t/f}}\]
Autotransformer Z and KVA Relations: