Single Phase Transformers
December 8, 2016
Categorised in: 1st Year Electrical
(1) Induced voltage:
$$ E = 4.44 f ϕ_m N $$
(2) Ratios:
Voltage ratio: $ V_1/V_2 $
Transformation ratio: $K = V_2/V_1 = E_2/E_1 = N_2 / N_1 $
Turns ratio: $N_1/N_2$
$$ I_1/I_2 = V_2 / V_1 $$
(3) Rating of Transformer:
$$ I_1 = {kVA 10^3}/{V_1} $$
(4) Copper Loss:
$$ P_{cu} = I_1_^2 R_1 + I_2_^2 R_2 $$
$$ P_{cu(HL)} = {(1/2)}^2 P_{cu(FL)} $$
(5) Iron Loss:
$P_i$ = Hysteresis Loss + eddy current loss
Hysteresis loss: $P_H = K_H B_m_^{1.67} f V$
Eddy current loss = $ I^2 $ x r
(6) Resistance transfered to primary side:
$$ R_{1T} = R_1 + R’_2 $$
where, $R’_2 = R_2/K^2$
(7) Resistance transfered to secondary side:
$$ R_{2T} = K^2 R_1 + R_2 $$
(8) Impedance:
$$ Z_1 = R_1 + j X_1 $$
where subscript 1 denotes primary, similarly 2 will denote secondary
(9) Efficiency:
$$η = {\text"Output Power"}/{\text"Input Power"} $$
$$ η= {\text"Output Power"}/{\text"Output Power + Losses"} $$
$$ η = {x kVA cosϕ_2 1000}/{(x kVA cosϕ_2 1000 ) + P_i + x^2 P_{cu}} $$
where, x = 1 for full load, 0.5 for half load, etc.
$kVA_{(load)} = kVA_{(max)} √{P_i/P_{cu}}$
(10) Voltage Regulation of Transformer:
$%Regulation = {E_2 – V_2}/{E_2} x 100 $
No load voltage = $E_2$ volts
Pratik Kataria is currently learning Springboot and Hibernate.
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