An instrumentation transformer has the following dimensions: A-c = 3.63 cm^2 I_c

Question

An instrumentation transformer has the following dimensions: A-c = 3.63 cm^2 I_c = 11.4 cm g = 0 cm (there is no air gap) The transformer is rated as follows: V1rms = 120 V (rated input voltage) V2rms = 33 V Rated Pload (avg) = 5 W Rated Load power factor = unity The core has the characteristics given below. Assume the following: At no load, when the transformer is excited with 60Hz voltage the maximum peak flux density should be 1.6 T Steel occupies 95% of the core area Mass-density of the steel is 7.65 g/cm^3 Assume that x11 pu = x12 pu = 0.02 The X/R ratio is 20 Find the required number of primary turns, N1 to the nearest turn Find the required number of secondary turns, N2 to the nearest turn Re-calculate the peak flux density using N1 from (a)

Explanation / Answer

a).We know that V=4.44fNBA where V=Voltage in rms,f=Frequency in Hertz,B=Fulx Density in Tesla,A=Area of cross section in meter square. Here V1=120, f1=60Hz, B=1.6T, A=3.63cm2 or 0.000363m2, Steal occupies 95% of the core area. So area factor =0.95 ..So effective area= 0.95X0.000363=0.000344m2. Thus putting all these values in the formula , we get V=4.44fNBA, we get N1=120/(4.44X60X1.6X0.000344)=816.3 . We know that number of turns should be integer. So, Number of turns = 817. b).We know that in any transfromer V1/V2=N1/N2. Here we have V1=120,V2=33,N1=817(as calculated). Thus putting these values in the formula V1/V2=N1/N2, we get N2=N1XV2/V1, Or N2=224.675 or N2=225(nearest). c).As per the formula V=4.44fNBA, to recalculate the Flux density we put the calculated value of N1 into this. We calculated N1=816.3 or 817(nearest value). By putting the values of "V1=120, f1=60Hz, N1=817, A=3.63cm2 or 0.000363m2, Steal occupies 95% of the core area. So area factor =0.95 ..So effective area= 0.95X0.000363=0.000344m2" , we get B=120/(4.44X60X0.000344X817)=1.602, which is almost equal to 1.6 T as given in the question.Recalclauted value is equal to the original value.

N1=817,N2=225 (Nearest Values) . Reclaculated value of Peak flux density=1.602T.

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