Important Formula of Design of Transformer - 1

 

EMF induced in the transformer winding E = 4.44fΦmN Where E = Induced emf F = Frequency Φm = Maximum flux density N = Number of turns

 

Volts per turn in the transformer ES / EP = 4.44fΦmNS / 4.44fΦmNP ES / EP = NS / NP ES / NS = EP / NP Volts per turn in the primary winding = Volts per turn in the secondary winding

 

The minimum winding diameter Dm of continuously transposed conductor ( CTC ) Dm = ( Pitch of transposition ) × ( Number of conductors ) / π Where pitch of transposition is distance between adjacent cross overs measured on one side of conductors and it is normally 15 times strip width.

 

Temperature rise θ = QC / S Where Q = Losses S = Heat dissipating area C = Cooling co – efficient

 

Current density δ = I / a Where δ = Current density I = Current a = Area

 

Conductor area in window AC = 2AT / δ Where AT = Ampere turns of windings                   = IPNP + ISNS                δ = Current density

 

Window space factor Kw = Conductor area in window / Total conductor area of window      = AC / AW

 

kVA rating of single phase transformer Q = 2.22fBmax δ KwAwAi × 10 – 3 kVA Where f = Frequency Bm = Maximum flux density δ= Current density Kw = Window space factor Aw = Window area Ai = Net core area

 

Rating of three phase transformer Q = 3.33fBmax δ KwAwAi × 10 – 3 kVA kVA rating of one phase Q = 4.44fΦmNPIP × 10 – 3     = 4.44fΦm ( AT ) × 10 – 3 Where Φm /  ( AT ) is constant for given transformer Voltage per turns Et = k √ Q Where k is constant = √ ( 4.44fr × 103 ) Where r = Φm /  ( AT ) Constant

 

Copper loss per meter3 = I2R = I2 ( ρL / a ) = ρ ( I2 L / a ) = ρ ( a2 δ2 L / a )    ( Current density δ = I / a ) = ρ δ2 ( aL ) = ρδ2 Where δ = Current density and            ρ = Resistivity of copper Copper loss per meter3 = ρ δ2

 

Specific iron loss is equal to iron loss per kg

 

Ratio of iron loss to copper loss Wi / Wc = Pi Gi / Pc Gc Where Pi = Iron loss per kg Pc = Copper loss per kg Gi = Weight of iron Gc = Weight of copper

 

Condition for minimum cost of transformer Weight of iron = Weight of copper Gi = Gc

 

Condition for minimum losses ( Maximum efficiency ) in the transformer Iron losses = Copper losses Wi = x2 Wc Where x = load at maximum efficiency occurs                     OR Wi / Wc = PiGi / PcGc x2 = PiGi / PcGc Gi / Gc = x2 ( Pc / Pi ) It is a condition for maximum efficiency in the transformer.

 

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