Power Transformer- Evolution of Equivalent Circuit & Vector Diagram. Important aspects â€“for being adept. Part-02
Published on 2021-01-29 16:40:11
A. Equivalent Circuit of an Ideal Transformer:
Fig. A1 shows the schematic diagram of a single-phase transformer. When the input voltage V1 is applied to the primary winding (N1 turns) under no-load condition, no-load current (Io) & a flux (Φm) is produced in the primary ckt & the magnetic core respectively. No-load primary current Io has two parts – loss component, Ih+e & it is called hysteresis and eddy current which is in phase with V1 & other part is magnetizing current Im which is 90o out of phase with V1. Magnetizing component Im has no contribution to any loss but it’s responsible for generating flux.
Fig. A2 shows the vector diagram under inductive load where current I2 lag voltage E2.
E1= Back emf induced in the primary winding.
At no load, the only loss is the iron loss due to hysteresis & eddy current loss. In the case of an ideal transformer, under also load condition winding resistance & leakage reactance are eliminated considering the infinite permeability of the core.
Fig. A3 shows the equivalent ckt of a ideal transformer where V1 = E1 & V2 = E2 .
B. Equivalent Circuit of a Real Transformer:
Fig. B1 shows the schematic diagram of a single-phase real transformer. When the input voltage V1 is applied to the primary winding (N1 turns), apart from the generation of no-load current(Io) & flux (Φ m ) in the primary side, loaded secondary side (N2 turns) will set up a current I2 (Fig. B3) whose value depends on the type of the load & secondary voltage. Current I2 in phase with secondary voltage V2 for resistive load, lag V2 for inductive load & I2 lead V2 in case of capacitive load. Secondary current will generate its magnetomotive force, mmf & a momentary flux Φ 2 which direction is opposite to the main flux Φ m .
Here , Φ 2 = Φ2 ‘
Why the no-load loss or iron loss always same?
Since the flux(Φ 2) produced by the secondary current & opposite flux( Φ2 ‘) of the same magnitude produced by the primary current (as discussed above) cancel each other & only the main flux (Φ m , produced at no load ) persists, we can conclude that no-load loss or iron loss is constant at all load ( full load, no-load, half load, etc) conditions.
Winding Resistance :
Actually, primary winding & secondary winding have some resistances & current flows through the windings make voltage drop (IR) and some losses. Therefore, primary induced back-emf E1 is less than V1 by an amount I1R1 whereas secondary induced back emf E2 is greater than V2 by an amount I2*R2 .
We can refer secondary resistance to primary & vice versa in the following way
Similarly, equivalent primary resistance as referred to secondary is
All the flux produced in the primary winding does not link the secondary winding. Apart from main flux Φ m , a part of magnetic flux (Φ L1 ) in the primary winding goes through the air path rather than magnetic core as the real iron core has not infinite permeability. This leakage flux is known as primary leakage flux (Φ L1 ) that does not link the secondary turns & proportional to primary amp-turns. The flux (Φ L1 ) is in phase with current I1 & induces a self-induced emf eL1.
Therefore, it is equivalent to an inductive coil in series with each winding so that voltage drop in the series coil is equal to that generated by that leakage flux.
Similar to resistance, X2’ = (N1/N2)^2 *X2 â®ž equivalent secondary reactance as referred to the primary.
And equivalent primary reactance as referred to secondary is
Fig.B2 & Fig.B3 show the vector diagram and equivalent circuit of a real transformer respectively.
If secondary resistance, R2 & leakage reactance, X2 are transferred to primary winding ( Fig.B4)
If primary resistance, R1 & leakage reactance, X1 are transferred to the secondary winding