CHAPTER 3.9: PROTECTION OF TRANSFORMERS

Example 3.9.2, Page number 635-636

In [1]:
#Variable declaration
V_lv = 220.0                 #LV side voltage of transformer(V)
V_hv = 11000.0               #HV side voltage of transformer(V)
ratio_CT = 600.0/(5/3**0.5)  #CT ratio on LV side of transformer

#Calculation
CT_pri = 600.0           #Primary CT
CT_sec = 5.0/3**0.5      #Secondary CT
I_1 = V_lv/V_hv*CT_pri   #Line current in secondary of transformer corresponding to primary winding(A)
I_2 = CT_sec*3**0.5      #Current in secondary of CT(A)

#Result
print('Ratio of CTs on 11000 V side = %.f : %.f ' %(I_1,I_2))
print('\nNOTE: ERROR: Mistake in representing the final answer in textbook solution')

Ratio of CTs on 11000 V side = 12 : 5 

NOTE: ERROR: Mistake in representing the final answer in textbook solution

Example 3.9.3, Page number 636

In [1]:
#Variable declaration
V_lv = 11.0*10**3       #LV side voltage of transformer(V)
V_hv = 66.0*10**3       #HV side voltage of transformer(V)
ratio_CT = 250.0/5      #CT ratio on LV side of transformer

#Calculation
V_hv_phase = V_hv/3**0.5          #HV side phase voltage(V)
ratio_main_T = V_hv_phase/V_lv    #Ratio of main transformer
I_2 = 250.0                       #Primary CT
I_1 = I_2/(ratio_main_T*3**0.5)   #Primary line current(A)
CT_sec = 5.0                      #Secondary CT
secondary_side = CT_sec/3**0.5    #HV side CT secondary

#Result
print('Ratio of CTs on high voltage side = %.1f : %.1f = (%.f/%.2f√3) : (%.f/√3) ' %(I_1,secondary_side,I_2,ratio_main_T,CT_sec))

Ratio of CTs on high voltage side = 41.7 : 2.9 = (250/3.46√3) : (5/√3)

Example 3.9.4, Page number 636

In [1]:
#Variable declaration
V_hv = 33.0           #HV side voltage of transformer(kV)
V_lv = 6.6            #LV side voltage of transformer(kV)
ratio_CT = 100.0/1    #CT ratio on LV side of transformer

#Calculation
CT_pri = 100.0              #Primary CT
CT_sec = 1.0                #Secondary CT
I_hv = V_lv/V_hv*CT_pri     #Line current on HV side(A)
I_lv = CT_sec/3**0.5        #Line current on LV side(A)

#Result
print('Ratio of protective CTs on 33 kV side = %.f : %.f/√3 = %.f : %.f ' %(I_hv,CT_sec,3**0.5*I_hv,I_lv*3**0.5))

Ratio of protective CTs on 33 kV side = 20 : 1/√3 = 35 : 1

Example 3.9.5, Page number 636-637

In [1]:
#Variable declaration
kVA = 200.0          #Transformer rating(kVA)
E_1 = 11000.0        #HV side voltage of transformer(kV)
E_2 = 400.0          #LV side voltage of transformer(kV)
ratio_CT = 500.0/5   #CT ratio on LV side of transformer
I_f = 750.0          #Fault current(A)

#Calculation
I_2 = 500.0                   #Primary CT
I_1 = 5.0                     #Secondary CT
I_1_T = E_2*I_2/(3**0.5*E_1)  #Primary current in transformer(A)
I_hv_T = I_1_T*3**0.5         #Equivalent line current on HV side(A)
I_pilot_lv = I_1*3**0.5       #Pilot current on LV side(A)

#Result
print('CT ratios on high voltage side = %.2f : %.2f ' %(I_hv_T,I_pilot_lv))
print('\nNOTE: Circulating current is not calculated')

CT ratios on high voltage side = 18.18 : 8.66 

NOTE: Circulating current is not calculated

Example 3.9.6, Page number 640

In [1]:
#Variable declaration
MVA = 50.0        #Transformer rating(MVA)
V_hv = 132.0      #HV side voltage of transformer(kV)
V_lv = 33.0       #LV side voltage of transformer(kV)
CT_sec = 1.0      #Secondary CT rating

#Calculation
I_FL = MVA*1000/(3**0.5*V_lv)                       #Full-load current(A)
CT_ratio_33kV = I_FL/CT_sec                         #CT ratio on 33 kV side
CT_ratio_132kV = (I_FL*V_lv/V_hv)/(CT_sec/3**0.5)   #CT ratio on 132 kV side

#Result
print('CT ratio on 33 kV side = %.f : 1 ' %CT_ratio_33kV)
print('CT ratio on 132 kV side = %.f : 1 = %.f√3 : 1 ' %(CT_ratio_132kV,CT_ratio_132kV/3**0.5))

CT ratio on 33 kV side = 875 : 1 
CT ratio on 132 kV side = 379 : 1 = 219√3 : 1