**1 Answer**

written 10 months ago by |

## Excitation phenomenon in three phase transformer

• Even though the secondary of transformer is open, transformer draws current from the supply when primary winding is excited by the rated voltage

• This current is not load current and is basically required to produce the core flux

• But due to non linearities of core material such as hysteresis and saturation, the no load current is not sinusoidal in nature

•The effect of hysteresis and saturation on the waveform of no load current is due to excitation current and the phenomenon is called excitation phenomenon in transformer

• Let V, be the rated voltage applied to the primary

• The resistive voltage drop I,R, is negligible

• The applied voltage and induced emf are sinusoidal in nature

• The flux must lag the applied voltage by 90°

• The no load current waveform can be obtained graphically from the hysteresis curve i.e. $\Phi-\mathrm{I}_{0}$, as shown in figure below

- In the steady state, the flux undergoes a cycle of magnetization and demagnetization due to sinusoidal voltage $\overparen{V_{1}}$ and traces a hysteresis loop as shown in figure (a)
- Consider various instants
- $\mathrm{Att} \mathrm{t}=\mathrm{t}_{0}, \Phi=-\Phi_{1}$ and no load current $\mathrm{I}_{0}$ is zero
- At $\mathrm{t}=\mathrm{t}_{1}$, flux is zero and $\mathrm{I}_{0}=\mathrm{I}_{01}$
- When $\Phi=\ldots \Phi_{1}$ at $\mathrm{t}=\mathrm{t}_{2}, \mathrm{I}_{0}=\mathrm{I}_{01}$
When $\Phi=\Phi_{2}$ at $\mathrm{t}=\mathrm{t}_{2}, \mathrm{I}_{0}=\mathrm{I}_{02}$

Now $\Phi_{2}$ value occurs twice while $\Phi$ increasing and decreasing

- But due to hysteresis at $\mathrm{t}=\mathrm{t}_{3}$, though $\Phi=\Phi_{2}$, $\mathrm{I}_{0}=\mathrm{I}_{03}$
- So $\mathrm{I}_{02} \mathrm{I}_{03}$ flows through $\Phi_{2}$
- When flux is maximum $\Phi_{\max }$, the current $\mathrm{I}_{0}$ is also at its maximum $\mathrm{I}_{0 \max }$
- The current $\mathrm{I}_{0}$ again becomes zero at $\Phi=\Phi_{1}$
- The negative half will be symmetrical to positive half of $\mathrm{I}_{0}$ as hysteresis loop is also symmetrical
- It can be seen that the $I_{0}$ waveform is non sinusoidal and having same peaks
- But it is odd symmetrical i.e. current and flux achieve their maxima simultaneouslv but current zeros are advanced with respect to flux
- Hence no load current has fundamental and odd harmonics
- The strongest is the third harmonic which is about 40% of fundamental
- $\text {And } \mathrm{I}_{0} \text { leads flux } \Phi \text { by a small angle } \alpha_{0}$
- $\text { Due to } \alpha_{0}, \mathrm{I}_{0} \text { has two components } \mathrm{I}_{\mathrm{c}} \text { and } \mathrm{I}_{\mathrm{m}}$
- This phase shift of $\alpha_{0}$ is caused due to hysteresis nature of $\Phi$ - $\mathrm{I}_{0}$ curve