Important Formula of Design of Transformer - 2

Effect of losses and output on linear dimension of transformer Let us consider that two transformer having linear dimensions in the ratio of x : 1 considering same flux density, current density, frequency and window space factor. The transformer A has dimension x with respect to transformer B. Output The output of transformer A = x4 times that of transformer B Losses The losses in the transformer A = x3 times that of transformer B.

 

Core area ( a ) Square core Ratio of net core area / Area of circumscribing circle = 0.58 Ratio of gross core area / Area of circumscribing circle = 0.64 Two stepped core Ratio of net core area / Area of circumscribing circle = 0.71 Ratio of gross core area / Area of circumscribing circle = 0.79

 

Relation between transformer rating and voltage per turn Et = k√ Q Where Q = Transformer kVA rating Et = Voltage per turn

 

Condition for minimum copper losses Current density in the primary winding = Current density in the secondary winding

 

Insulation thickness ( a )  Between winding earth and LV and HV winding Insulation thickness = 5 + 0.9 kV mm kV = kilo voltage between winding and earth      = kilo voltage between windings

 

Cross over winding It should be designed such that 2NCL Et > 800 V Where NCL = Number of conductor per layer               Et = Voltage per turn

 

Continuous disc / Cross over winding The voltage per coil should not be more than 800 – 1000 V for continuous disc / cross over winding Number of coils > = V / ( 800 to 1000 V )

 

The shunt capacitance of winding relative to ground is proportional to its length and series capacitance is inversely proportional to the length.

 

L’ Hospital’s rule ( dv / dx ) = V / L constant If the shunt capacitance is zero, the voltage is uniformly distributed over the winding. The voltage gradient at the line end is α times the value of voltage gradient to the uniform voltage distribution. Where α = √ ( Cg / Cs ) Where Cg = Shunt capacitance Cs = Series capacitance

 

The number of layers in the cross over winding are calculated on the basis that the maximum voltage between layers should not exceed 300 V.

 

The voltage distribution across insulation is improved by decreasing shunt capacitance or increasing series capacitance.

 

Window space factor Kw = 10 / ( 30 + kV ) kV = High voltage winding in kV

 

Window area = Hw × Ww = Height of window × Width of window

 

Width of window for optimum output D = 1.7d Where d = Diameter of circumscribing circle D = Distance between center to center between adjacent limbs

 

You may also like :

Travelling waves MCQs – 1

Travelling waves MCQs – 2

Travelling waves MCQs – 3

Travelling waves MCQs – 4