A-100 kVA transformer has 400 turns on the primary and 80 turns on the secondary. The primary and secondary resistances are 0.3 Ω and 0.01 Ω respectively and the corresponding leakage reactances are 1.1 and 0.035 Ω respectively. The supply voltage is 2200 V. Calculate
(i) equivalent impedance referred to primary
(ii) the voltage regulation and the secondary terminal voltage for full load having a power factor of 0.8 leading.
If you are noticing some error in problems kindly comment below.Thanks
Given
KVA = 100
N1 = 400
N2 = 80
R1 = 0.3 Ω
R2 = 0.01 Ω
X1 = 1.1 Ω
X2 = 0.035 Ω
V1 = 2200 V
To find
(i) Equivalent impedance referred to primary
(ii) The voltage regulation and the secondary terminal voltage for full load having a power factor of 0.8 leading.
Solution
As we know that Voltage transformation ratio,
K = N2 / N1
= 80 / 400
= 0.2
Equivalent Resistance referred to primary
R01 = R1 + (R2 / K2)
= 0.3 + (0.01 / 0.22)
= 0.55 Ω
Equivalent Reactance referred to primary
X01 = X1 + (X2 / K2)
= 1.1 + (0.035 / 0.22)
= 1.975 Ω
i) Equivalent Impedence referred to primary
Z01 = R01 + j X01
= 0.55 + j 1.975
= 2.05 ∠ 74.44°
ii) Equivalent Impedence referred to secondary
Z02 = K2 x Z01
= 0.22 x (0.55 + j 1.975)
= 0.022 + j 0.079
So R02 = 0.022 and X02 = 0.079 [Z02 = R02 + j X02]
No load secondary voltage ,
V2 = K x V1
= 0.2 X 2200
= 440 V
Full load current,
I2 = KVA / V2
= 100,000 / 440
= 227.3 A
F.L Voltage drop across secondary = I2 (R02 cos Ф - X02 sin Φ)
= 227.3(0.022 x 0.8 - 0.079 x 0.6)
= - 6.77 V
So Voltage regulation % = (- 6.77 x 100) / 440
= - 1.54
Secondary terminal voltage = 440 - (-6.67)
= 446.7 V
(i) equivalent impedance referred to primary
(ii) the voltage regulation and the secondary terminal voltage for full load having a power factor of 0.8 leading.
If you are noticing some error in problems kindly comment below.Thanks
KVA = 100
N1 = 400
N2 = 80
R1 = 0.3 Ω
R2 = 0.01 Ω
X1 = 1.1 Ω
X2 = 0.035 Ω
V1 = 2200 V
To find
(i) Equivalent impedance referred to primary
(ii) The voltage regulation and the secondary terminal voltage for full load having a power factor of 0.8 leading.
Solution
As we know that Voltage transformation ratio,
K = N2 / N1
= 80 / 400
= 0.2
Equivalent Resistance referred to primary
R01 = R1 + (R2 / K2)
= 0.3 + (0.01 / 0.22)
= 0.55 Ω
Equivalent Reactance referred to primary
X01 = X1 + (X2 / K2)
= 1.1 + (0.035 / 0.22)
= 1.975 Ω
i) Equivalent Impedence referred to primary
Z01 = R01 + j X01
= 0.55 + j 1.975
= 2.05 ∠ 74.44°
ii) Equivalent Impedence referred to secondary
Z02 = K2 x Z01
= 0.22 x (0.55 + j 1.975)
= 0.022 + j 0.079
So R02 = 0.022 and X02 = 0.079 [Z02 = R02 + j X02]
No load secondary voltage ,
V2 = K x V1
= 0.2 X 2200
= 440 V
Full load current,
I2 = KVA / V2
= 100,000 / 440
= 227.3 A
F.L Voltage drop across secondary = I2 (R02 cos Ф - X02 sin Φ)
= 227.3(0.022 x 0.8 - 0.079 x 0.6)
= - 6.77 V
So Voltage regulation % = (- 6.77 x 100) / 440
= - 1.54
Secondary terminal voltage = 440 - (-6.67)
= 446.7 V
In first answer how 74.44 degrees calculated??
ReplyDeleteRectangular form of a vector, v = 0.55 + j 1.975. where 0.55 is the real axis value and 1.975 is the value of an imaginary axis.
ReplyDeleteTo find the Phasor magnitude V, calculate the modulus of vector a + jb.
Magnitude of vector, V = √ (0.55)2 + (1.975)2. ----- 2 is square.
= √ 0.3025 + 3.900
= 2.05
To find the angle of a vector with respect to the horizontal axis,
θ = tan-1 (1.975/0.55)
= tan-1 3.5909
= 1.299 radian
To convert from radians to degrees, you simply have to multiply the radian value by 180/π
sso 1.299 radian = 1.299 x (180/π)
= 74.44 deg