- The primary winding of a transformer draws an exciting current that establishes flux in the core. This flux induces an emf in both the primary and secondary windings. - The maximum flux in a transformer's core is determined by the voltage-to-frequency ratio of the supply. An example calculates the maximum flux for a transformer excited by a 60Hz, 200V source and when the frequency is reduced to 50Hz. - The exciting current on no-load has two components - a magnetizing current in phase with flux and a core-loss current in phase with the induced emf. The total current lags the induced emf by a small angle.

1. Transformer on No load

2. Transformer on-no load

3. Transformer on-no load
• The primary winding draws a small amount of alternating current of
instantaneous value i0, called the exciting current, from the voltage
source.
• The exciting current establishes flux ϕ in the core all of which is
assumed to be confined to the core i.e., there is no leakage of flux.
• Applying kvl on the primary winding,
𝑣1 = 𝑒1 (𝑎𝑠𝑠𝑢𝑚𝑖𝑛𝑔 𝑡ℎ𝑎𝑡 𝑡ℎ𝑒 𝑤𝑖𝑛𝑑𝑖𝑛𝑔 ℎ𝑎𝑠 𝑧𝑒𝑟𝑜 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒)

4. Transformer on-no load
• The primary winding will have flux linkages λ1 = 𝑁1ϕ
• This flux induces an emf in the primary winding which will be
given as
𝑒1 =
𝑑λ1
𝑑𝑡
= 𝑁1
𝑑ϕ
𝑑𝑡

5. Transformer on-no load
• The induced emf, and the flux will be sinusoidal just as the voltage
source
ϕ = ϕ𝑚𝑎𝑥 sin ω𝑡
• Where ϕ𝑚𝑎𝑥 is the maximum value of the core flux
ω =2πf in rad/s (f =frequency of voltage source)
• The emf induced in the primary winding will be
• 𝑒1 = 𝑁1
𝑑ϕ
𝑑𝑡
= ω𝑁1ϕ𝑚𝑎𝑥 cos ω𝑡
• The rms Value of the induced emf will be given by
𝐸1 = 2πf𝑁1ϕ𝑚𝑎𝑥 = 4.44f𝑁1ϕ𝑚𝑎𝑥

6. Transformer on-no load
• Since 𝐸1 = 𝑉1, then Maximum Flux will be given as
ϕ𝑚𝑎𝑥 =
𝐸1 = (𝑉1)
4.44𝑓𝑁1
1
• So the maximum flux in a transformer is determined by the voltage/frequency
ratio at which it is operating
• Equation (1) is true for any electromagnetic device operating with
sinusoidally varying ac assuming all other assumptions are the same.
• The flux produced in the primary also links the secondary coil and induces an
emf of
𝑒2 = 𝑁2
𝑑ϕ
𝑑𝑡
• 𝑒1and 𝑒2 are in Phase as both are induced by the same flux.

7. Example
The Primary of a transformer has 200 turns and is excited by a 60 Hz,
200V source.
• What is the maximum value of the core flux?
• If the supply frequency is reduced to 50Hz, what will be the maximum
value of the core flux

8. Transformer on-no load
• The Excitation current 𝐼𝑜 will be
made up of two components, 𝐼𝑚
and 𝐼𝑖
• 𝐼𝑚 is the component of exciting
current that is magnetizing in
nature and is proportional to the
sinusoidal flux and in phase with
it. It lagging the induced emf by
90°.

9. Transformer on-no load
• The component 𝐼𝑖 comes about
due to the presence of Hysterisis
and phenomenon of eddy
currents. It is in phase with E1
• Thus, the exciting current lags
the induced emf by an angle θ
slightly less than 90° as shown in
the phasor diagram

10. Transformer on-no load

11. Transformer on-no load
• From the phasor diagram , the core-loss is given by
• From the no-load phasor diagram, the parallel circuit model of exciting
current can be easily imagined where in conductance Gi accounts for
core-loss current Ii and inductive susceptance Bm for magnetizing
current Im.
• Both these currents are drawn at induced emf E1 = V1 for resistance-
less,

12. Transformer on-no load

13. Example
A transformer on no-load has a core-loss of 50 W, draws a current of 2 A
(rms) and has an induced emf of 230 V (rms).
• Determine the no-load power factor, core-loss current and magnetizing
current.
• Also calculate the no-load circuit parameters of the transformer.
Neglect winding resistance and leakage flux.