3. An instrumentation transformer has the following dimensions: Ac 3.63 cm2 11.4

Question

3. An instrumentation transformer has the following dimensions: Ac 3.63 cm2 11.4 cm g 0 cm (there is no air gap) The transformer is rated as follows: Virms 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/cm3 Assume that xllpu Fx12pu 0.02 The X/R ratio is 20 (a Find the required number of primary turns, NI to the nearest turn (b) Find the required number of secondary turns, N2 to the nearest turn (c) Re-calculate the peak flux density using Ni from (a) (d) Re-calculate the secondary voltage using NI and N2 from (a) and (b) (e) Calculate the base quantities based on Virms and Rated Pload (avg) (f Assuming that rl r2' and xll x12', find rl, r2,xll,x12 (g) Find the load resistance, rL and rL referred to the primary side of the transformer (h) Find the core loss and exciting volt-amperes (i) Calculate the exciting current G) Calculate the Core-loss component of current from the exciting current (k) Calculate the magnetizing component of the exciting current (l) Calculate the core loss resistance (m)Calculate the magnetizing impedance (n) Find the input current and input power factor (o) Find the secondary current and, using it, calculate load power and load voltage referred to the primary, V2' (p) Calculate the actual transformer regulation (q) Calculate the transformer efficiency (r) Show the transformer equivalent circuit using p.u. values (s) Show the phasor of V2' in per unit using the phasor diagram

Explanation / Answer

(b)we know that Ac=V2rms*10^4/(Kf*Bac*f*N2),I1=Pload(avg)/V1rms=41.66mA I2=Pload(avg)/V2rms=151.51mA ,Kf =X/R=20,f=60H,Bac=1.6T,Ac=3.63 cm^2 substituting we get N2=47*10^4 turns (a)N1=N2*(I1/I2)=13 *10^4 turns (d)V2rms=V1rms*(N2/N1)=433.84V (c)Bac=V1rms/(4.44*f*N1*A)=0.00954T

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