Operation of Transformer Flashcards
Transformation Ratio?
k = N2/N1 k = E2/E1
Relation between transformation ratio (k) and turns ratio?
Turns ratio = 1/k
The transformation ratio is defined as the ratio of the secondary voltage to the primary voltage.
And
Turns Ratio is the number of turns in primary winding to the secondary winding
In 5KVA, 400V/200V Transformer, what is E1 and E2?
E1 = 400V E2 = 200V
For the same rating transformer, relation between frequency and specific weight?
Frequency ∝ 1/ Specific Weight
Components of no-load current?
Io = Iw + Iμ
Iw - Active component or wattfull component of current
Iμ - Reactive component or wattless component of current
What is the iron loss component of NL current?
Iw - It is drawn from the source to supply the power required for iron loss.
What is the magnetizing component of NL current?
Iμ - Responsible to create the flux in core
Iw and Iμ formulas?
Iw = Io cos Φo
It is always in phase with applied voltage.
Iμ = Io sin Φo
It is always in quadrature with applied voltage.
Percentage of Iw and Iμ in FL current? Io?
Iw - 1-2% of FL current
Iμ - 4-5% of FL current
Io - 5-6% of FL current
No-load current formula?
Io = √Iw2 + Iμ2
No-load power is also called? formula?
No-load power = Iron losses = Core losses = V1 x Iw
Where is the no-load branch placed?
The no-load current is never transferred from primary to secondary, hence the shunt branch/no-load branch is parallel to the primary winding.
No-load branch resistance and reactance formulas?
Ro = V1/ Iw Xo = V1/Iμ
Parameters in the operation of the transformer?
Io - NL current
I1 - Primary current
I2 - Secondary current - Load current
I1’ - Load component of secondary current
Φo - No load flux - Main flux
Φ1 - Primary flux
Φ2 - Load component of secondary flux - Load angle
Φ1’ - Load component of primary flux
V1 - Supply voltage
V2 - Secondary terminal voltage - Load voltage
Operation of transformer?
Iμ produces flux (Φmain) that links with the secondary winding producing emf.
The emf in the secondary winding sets up a current (I2) which in turn produces its own flux (Φ2) opposing the main flux.
The resultant flux, Φr = Φmain - Φ2
leading to a drop in (V1-E1) to compensate for this, an additional current I1’ is drawn.
I1’ produces flux Φ1’ equal to Φ2.
Now, the resultant flux is Φr = Φmain - Φ2 + Φ1’
Φ1’ cancels out Φ2 ; so Φr = Φmain
Hence, the transformer is a constant flux machine.
Equivalent parameters referred to the primary side?
V2' = V2/k I2'= I2 x k
R01 = R1 + R2' X01 = X1 + X2' Z01 = Z1 +Z2'
R2' = R2/sq(K) X2' = X2/sq(K) Z2' = Z2/sq(K)
Equivalent parameters referred to the secondary side?
V2' = V2 x k I2'= I2/k
R02 = R1' + R2 X02= X1' + X2 Z02 = Z1' +Z2
R1' = R1 x sq(K) X1' = X1 x sq(K) Z1' = Z1 x sq(K)
Total Cu losses formula?
- (I1)2xR1+ (I2)2 xR2
Total Pu resistance drop?
R01 pu = I1R01/E1
&
R02 pu = I2R02/E2
where:
I1 = KVA / E1
I2 =KVA / E2
Relation of pu resistances and % resistances in a trasformer?
R01 ≠ R02
But,
R01 pu = R02 pu
% R01 pu = % R02 pu
What is useful flux? and leakage flux?
In a transformer, both primary and secondary currents produce flux. The flux Ф which links both the windings is the useful flux and is called mutual flux. It is independent of load and remains constant.
However, the primary current would produce some flux Фl1 which would not link the secondary winding. Similarly, secondary winding would produce Фl2 that would not link the primary winding. The flux such as Фl1 or Фl2 which links only one winding is called leakage flux. They do not participate in the energy conversion process.
What is the effect of leakage flux in the operation of the transformer?
Фl1 produces Ex1 and Фl2 produces Ex2.
These emf generated do not participate in the energy conversion process and can be considered as voltage drop.
This drop is given by: I1 X1 and I2X2
The reason to choose reactance over resistance is that flux causes a drop in voltage not any losses.
