# CHAPTER 3.10: PROTECTION OF TRANSMISSION LINE, SHUNT INDUCTORS AND CAPACITORS¶

## Example 3.10.1, Page number 647-648¶

In :
#Variable declaration
G2_per = 70.0              #G2 is fed at 70% distance from A in section AB(%)
X_T = 10.0                 #Transformer reactance(%)
zone_1_per = 80.0          #Setting for first zone(%)
zone_2_per = 50.0          #Setting for second zone(%)
CT_ratio = 400.0/5         #CT ratio
PT_ratio = 166000.0/110    #PT ratio
Z_AB = complex(20.0,60.0)  #Section AB impedance(ohm)
Z_BC = complex(10.0,25.0)  #Section BC impedance(ohm)
MVA = 10.0                 #Transformer rating(MVA)
kV_hv = 166.0              #HV side voltage(kV)
kV_lv = 33.0               #LV side voltage(kV)

#Calculation
#Case(i) Without infeed
Z_sec_1 = zone_1_per/100*Z_AB*CT_ratio/PT_ratio                 #First zone setting(ohm)
Z_BC_hv = Z_BC*(kV_hv/kV_lv)**2                                 #Z_BC on 166 kV base(ohm)
Z_T = 1j*10*X_T*kV_hv**2/(MVA*1000)                             #Transformer impedance(ohm)
Z_sec_2 = (Z_AB+zone_2_per/100*Z_BC_hv+Z_T)*CT_ratio/PT_ratio   #Second zone setting(ohm)
Z_sec_3 = (Z_AB+Z_BC_hv+Z_T)*CT_ratio/PT_ratio                  #Third zone setting(ohm)
#Case(ii) With infeed
I_AB = 2.0                                                                                           #Current ratio
Z_zone_1 = (G2_per/100*Z_AB)+I_AB*(zone_1_per-G2_per)/100*Z_AB                                       #First zone impedance(ohm)
Z_1 = Z_zone_1*CT_ratio/PT_ratio                                                                     #First zone setting(ohm)
Z_zone_2 = (G2_per/100*Z_AB)+I_AB*(((zone_1_per-zone_2_per)/100*Z_AB)+(zone_2_per/100*Z_BC_hv)+Z_T)  #Second zone impedance(ohm)
Z_2 = Z_zone_2*CT_ratio/PT_ratio                                                                     #Second zone setting(ohm)
under_reach = Z_zone_2-(Z_AB+zone_2_per/100*Z_BC_hv+Z_T)                                             #Under-reach due to infeed(ohm)
Z_zone_3 = (G2_per/100*Z_AB)+I_AB*(((zone_1_per-zone_2_per)/100*Z_AB)+Z_BC_hv+Z_T)                   #Third zone impedance(ohm)
Z_3 = Z_zone_3*CT_ratio/PT_ratio                                                                     #Third zone setting(ohm)

#Result
print('Case(i)  Without infeed:')
print('         First zone relay setting = (%.2f + %.2fj) ohm' %(Z_sec_1.real,Z_sec_1.imag))
print('         Second zone relay setting = (%.1f + %.1fj) ohm' %(Z_sec_2.real,Z_sec_2.imag))
print('         Third zone relay setting = (%.1f + %.1fj) ohm' %(Z_sec_3.real,Z_sec_3.imag))
print('Case(ii) With infeed:')
print('         First zone relay setting = (%.3f + %.2fj) ohm' %(Z_1.real,Z_1.imag))
print('         Second zone relay setting = (%.1f + %.1fj) ohm' %(Z_2.real,Z_2.imag))
print('         Third zone relay setting = (%.1f + %.fj) ohm' %(Z_3.real,Z_3.imag))
print('\nNOTE: ERROR: Calculation mistake in Z_BC. Hence, changes in the obtained answer from that of textbook')

Case(i)  Without infeed:
First zone relay setting = (0.85 + 2.54j) ohm
Second zone relay setting = (7.8 + 34.6j) ohm
Third zone relay setting = (14.5 + 51.3j) ohm
Case(ii) With infeed:
First zone relay setting = (0.954 + 2.86j) ohm
Second zone relay setting = (14.8 + 66.9j) ohm
Third zone relay setting = (28.2 + 100j) ohm

NOTE: ERROR: Calculation mistake in Z_BC. Hence, changes in the obtained answer from that of textbook


## Example 3.10.2, Page number 648¶

In :
#Variable declaration
CT_ratio = 300.0/5          #CT ratio
PT_ratio = 166000.0/110     #PT ratio
Z_AB = complex(40.0,160.0)  #Section AB impedance(ohm)
Z_BC = complex(7.5,15.0)    #Section BC impedance(ohm)
kV_hv = 166.0               #HV side voltage(kV)
kV_lv = 33.0                #LV side voltage(kV)
MVA = 5.0                   #Transformer rating(MVA)
X_T = 6.04                  #Transformer reactance(%)

#Calculation
Z_T = 1j*10*X_T*kV_hv**2/(MVA*1000)   #Tranformer impedance(ohm)
Z_fault = Z_AB+Z_T                    #Fault impedance(ohm)
Z_sec = Z_fault*CT_ratio/PT_ratio     #Relay setting for primary protection(ohm)
Z_BC_hv = Z_BC*(kV_hv/kV_lv)**2       #Z_BC on 166 kV base(ohm)
Z = Z_AB+Z_T+Z_BC_hv                  #For backup protection of line BC(ohm)
Z_sec_set = Z*CT_ratio/PT_ratio       #Relay setting(ohm)

#Result
print('Impedance seen by relay = (%.f + %.fj) ohm' %(Z_fault.real,Z_fault.imag))
print('Relay setting for high speed & backup protection = (%.1f + %.2fj) ohm' %(Z_sec_set.real,Z_sec_set.imag))

Impedance seen by relay = (40 + 493j) ohm
Relay setting for high speed & backup protection = (9.1 + 34.69j) ohm