# CHAPTER 3.7: PROTECTIVE RELAYS¶

## Example 3.7.1, Page number 595-596¶

In :
#Variable declaration
I_setting = 150.0   #Current setting of IDMT(%)
t_mult = 0.5        #Time multiplier setting
ratio_CT = 500.0/5  #CT ratio
CT_sec = 5.0        #Secondary turn
I_f = 6000.0        #Fault current

#Calculation
I_sec_fault = I_f/ratio_CT                #Secondary fault current(A)
PSM = I_sec_fault/(CT_sec*I_setting/100)  #Plug setting multiplier
t = 3.15                                  #Time against this PSM(sec). From graph E7.1 in textbook page no 595
time_oper = t*t_mult                      #Operating time(sec)

#Result
print('Time of operation of the relay = %.3f sec' %time_oper)

Time of operation of the relay = 1.575 sec


## Example 3.7.2, Page number 596¶

In :
#Variable declaration
ratio = 525.0/1     #CT ratio
CT_sec = 1.0        #Secondary turn
t_mult = 0.3        #Time multiplier setting
I_f = 5250.0        #Fault current(A)

#Calculation
I_sec_fault = I_f/ratio            #Secondary fault current(A)
PSM = I_sec_fault/(1.25*CT_sec)    #Plug setting multiplier
t = 3.15                           #Time against this PSM(sec). From graph E7.1 in textbook page no 595
time_oper = t*t_mult               #Operating time(sec)

#Result
print('Time of operation of the relay = %.3f sec' %time_oper)

Time of operation of the relay = 0.945 sec


## Example 3.7.3, Page number 596¶

In :
#Variable declaration
MVA = 20.0            #Transformer MVA
kV = 11.0             #Bus bar rating(kV)
CT_trans = 1000.0/5   #Transformer CT
CT_cb = 400.0/5       #Circuit breaker CT
ps = 125.0            #Plug setting(%)
ts = 0.3              #Time setting
I_f = 5000.0          #Fault current(A)
t_margin = 0.5        #Discriminative time margin(sec)

#Calculation
I_sec_fault = I_f/CT_cb                          #Secondary fault current(A)
CT_cb_sec = 5.0                                  #Secondary turn
PSM = I_sec_fault/(ps/100*CT_cb_sec)             #Plug setting multiplier
t = 2.8                                          #Time against this PSM(sec). From graph E7.1 in textbook page no 595
time_oper = t*ts                                 #Operating time of feeder relay(sec)
I_sec_T = I_ol/CT_trans                          #Secondary current(A)
CT_T_sec = 5.0                                   #Secondary turn of transformer
PSM_T = I_sec_T/CT_T_sec                         #Minimum plug setting multiplier of transformer
I_sec_T1 = I_f/CT_trans                          #Secondary fault current(A)
ps_T1 = 1.5                                      #Plug setting as per standard value
PSM_T1 = I_sec_T1/(CT_T_sec*ps)                  #Plug setting multiplier of transformer
t_T1 = 7.0                                       #Time against this PSM(sec). From graph E7.1 in textbook page no 595
time_setting = (time_oper+t_margin)/t_T1         #Time setting of transformer

#Result
print('Operating time of feeder relay = %.2f sec' %time_oper)
print('Minimum plug setting of transformer relay, P.S > %.2f ' %PSM_T)
print('Time setting of transformer = %.3f ' %time_setting)

Operating time of feeder relay = 0.84 sec
Minimum plug setting of transformer relay, P.S > 1.36
Time setting of transformer = 0.191


## Example 3.7.4, Page number 596-597¶

In :
#Variable declaration
I_f = 2000.0         #Fault current(A)
ratio_CT = 200.0/1   #CT ratio
R_1 = 100.0          #Relay 1 set on(%)
R_2 = 125.0          #Relay 2 set on(%)
t_margin = 0.5       #Discriminative time margin(sec)
TSM_1 = 0.2          #Time setting multiplier of relay 1

#Calculation
CT_sec = 200.0                         #CT secondary
PSM_1 = I_f*100/(CT_sec*R_1)           #PSM of relay 1
t_1 = 2.8                              #Time against this PSM(sec). From graph E7.1 in textbook page no 595
time_oper_1 = TSM_1*t_1                #Operating time of relay with TSM of 0.2(Sec)
PSM_2 = I_f*100/(CT_sec*R_2)           #PSM of relay 2
t_2 = 3.15                             #Time against this PSM(sec). From graph E7.1 in textbook page no 595
actual_time_2 = time_oper_1+t_margin   #Actual time of operation of relay 2(sec)
TSM_2 = actual_time_2/t_2              #Time setting multiplier of relay 2

#Result
print('Time of operation of relay 1 = %.2f sec' %time_oper_1)
print('Actual time of operation of relay 2 = %.2f sec' %actual_time_2)
print('T.S.M of relay 2 = %.4f' %TSM_2)

Time of operation of relay 1 = 0.56 sec
Actual time of operation of relay 2 = 1.06 sec
T.S.M of relay 2 = 0.3365


## Example 3.7.6, Page number 611¶

In :
#Variable declaration
I_min = 0.1          #Relay minimum pick up current(A)
slope = 10.0         #Slope characteristic(%)
CT_ratio = 400.0/5   #CT ratio
I_1 = 320.0          #Current(A)
I_2 = 304.0          #Current(A)

#Calculation
I_op_coil = (I_1-I_2)/CT_ratio           #Current in operating coil(A)
I_re_coil = 1.0*(I_1+I_2)/(2*CT_ratio)   #Current in restraining coil(A)
I_re_coil_slope = I_re_coil*slope/100    #Current in restraining coil with slope(A)

#Result
if(I_op_coil<I_re_coil_slope):
print('Relay will not trip the circuit breaker')
else:
print('Relay will trip the circuit breaker')

Relay will not trip the circuit breaker