transformer picture

Finding loss

Now, voltage regulation (VR)=E_rcos  +E_xsin

 E_r=I_pR_p/V_P = 3.787*45.44/11000 =0.0156pu

 E_x = I_pX_p/V_P =3.787*198.742/11000 =0.0684 pu

Let, power factor , cos =0.9

                              sin  =0.43S

VR = 0.0156*0.8 +0.0684*0.6 =  0.0438

                                                         =0.0438*100% =4.38%

                                 (for distribution transformer  <5%)

                                 (for power transformer  <10%)

FOR COPPER LOSS

P_c=I²R =3*I_p²*R_p =1955 w

As stray loss also variable ,total copper loss including stary loss 15% greater

                                                                                                 =1.15*1955 =2248.25W

FOR IRON LOSS

  For hot rolled material of transformer core :

Density of lamination 7.6*10³ kg/m³

Weight of 3-limbs = 3*H_w*A_p7.6*10³

                                   =172.43kg

Weight of 2-yoke =2*A_gi*W*density

                                 =258.248kg

Specific iron loss for hot rolled =1.8w/kg

Now, iron loss in limbs = weight of limbs *specific iron loss

                                          = 172.43*1.8 = 310.359 w

Flux density for yoke =1wb/m²

Core loss in yoke = 258.248*1.2 = 309.897 w

Total iron loss,P_i = (309.897+310.389)

                                =620.28 w

   total loss = P_i + P_c    =620.28+ 2248.25 = 2868.53 w

FOR EFFICIENCY

Now, efficient (Ƞ ) =( output/(output +losses))*100%

                            =(125/(125+2868/0.9))*100%

                             =97.51%

Condition of maximum efficiency, x=   = 0.5255

Thus, maximum efficiency occurs at 52.55% of full load, which is almost good for distribution transformer.

Finding reactance

FOR LEAKAGE REACTANCE

Now , leakage reactance refers to primary

   X_p=2 *f* *T_p²*L_mt/L_c*(a+(b_p +b_s)/3)

  Where L_mt=length of mean turns

                 L_c=height of winding

                  b_p=radial depth of primary

                   b_s=radial depth of secondary & a= width of insulation

L_mt= d_pt

      = (inside of dia of LV + outside of HV winding)/2

      = *(176.62*293.65)/2

      = 738.72mm

L_c =axial height of primary

L_cs= axial height of secondary

Now, X_p=2* *50*4 *10^-7*2310²*(738.72/363.125)*(15+(47.75+15)/2)

               =198.742 ohm

PU leakage reactance = (3.787*198.742)/11000 = 0.0684