Efficiency of a transformer

Condition for the maximum efficiency

All-Day Efficiency

• Power transformer (at generating station) and Distribution transformer (distribution substation)

• Power transformers are switched in or out of the circuit depending upon the load to be handled

• Distribution transformer is never switched off remain irrespective of the load

• In such case, constant loss continues to be dissipated

• Concept of energy based efficiency arise - "all day efficiency"

  \[\begin{aligned} \%\mbox{all-day}\eta & =\dfrac{\mbox{Output energy in KWh during a day}}{\mbox{Input energy in KWh during a day}}\times100\\ & =\dfrac{\mbox{Output energy in KWh during a day}}{\mbox{Output energy +Energy spent for total losses}}\times100 \end{aligned}\]

Auto-Transformer

• Transformer with one winding only

• Part of the winding is common to both primary and secondary

• No electrical isolation as in 2-winding transformer

• Theory and operation remains similar

• Because of one winding, uses less copper and hence cheaper

• It is used where transformation ratio varies little from unity

  

  

  Saving of Cu

• Volume (or weight) \(\propto\) length and area of cross-section
  length of conductor \(\propto\) number of turns
  cross-section depends on current
  Weight \(\propto\) product of current and number of turns

  Wt. of Cu in section AC is \(\propto\) \((N_1-N_2)I_1\)
  Wt. of Cu in section BC is \(\propto\) \(N_2(I_2-I_1)\)
  \(\therefore\) Total Wt. of Cu \(\propto\) \((N_1-N_2)I_1+N_2(I_2-I_1)\)
  

• \[\therefore \dfrac{\mbox{Wt. of Cu in auto-transformer}}{\mbox{Wt. of Cu in ordinary transformer}} = \dfrac{(N_1-N_2)I_1+N_2(I_2-I_1)}{N_1I_1+N_2I_2} = (1-K)\]
  Total Wt. of Cu \(N_2I_2\)\(\propto\)
  Wt. of Cu in primary If a 2-winding T/F perform the same task, then

  \(\Rightarrow\) \(W_a\) = \((1-K) \times W_0\)

  \[\boxed{\text{Saving}=W_0-W_a=W_0-(1-K)W_0=KW_0}\]

  Hence, saving will increase as \(K\) approaches unity
  \(\Rightarrow\) Power transferred inductively is

  \[\boxed{P_{ind}=Input\times(1-K)}\]

  \(\Rightarrow\) The rest of the power is conductively transferred

  \[\boxed{P_{cond}=\text{Input}\times K}\]

  Advantages of Auto transformer

  • Less costly

  • Better regulation

  • Low losses as compared to 2-winding T/F of the same rating

  Disadvantages of Auto transformer

  • The secondary winding is not insulated from primary so if a low supply voltage is used from a high voltage and if a break occurs in secondary winding then full primary voltage comes across the secondary terminal which is dangerous to the operator and the equipment.

  • used only in limited places where a slight variation of the output voltage from input voltage is required.

  Applications of Auto transformer

  • Used as a starter to give 50-60% of full voltage to the stator of a squirrel cage induction motor during starting

  • used to give a small boost to a distribution cable, to correct the voltage drop

  • used as a voltage regulator

  • in power T & D system and also in audio system and railways