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Table of Contents 

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The 51OC element implements the inversetime overcurrent protection logic. The input operating quantity can be the RMS of phase current, ground current or symmetrical components.
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The relay resets once the input current drops to below the pickup current value. The reset can be instantaneous, which means the reset time is not according to an inverse curve and is an instant zero. Or it can be timed, which means the reset time is according to a reset inverse curve and its defined characteristics.
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If the input current is above the pickup level and custom curves are not used, the relay's tripping time is calculated based on the following equation:
Mathblock  

 
\Large T(Trip) = TD*(\frac{A}{M^P1}+B) + K 
The reset time of the relay can be calculated based on this equation in an inverse curve:
Mathblock  

 
\Large T(Reset) = TD*(\frac{T_r}{1M^P}) 
Mathblock  

 
\Large TD = Time Dial, M = \frac{I}{I(pickup)}

TD is a time dial multiplier, M is the value of the input current divided by the pickup current, and the rest of the parameters are characteristics of the inverse curve that define it. The parameters can be from standard curves such as the US standard and IEC standard curves, or they can be specified by the user to create their own inverse curve. As mentioned before, the reset curve only applies if the relay's reset setting is timed and not instantaneous.
The US standard coefficients are based on the values used by SEL relays and it follows the IEEE C37IEEE C37.1122018 equation. The IEC curves use the same equation and coefficients stated by the IEC 60255 standard for inverse time overcurrent relays. [1]
Cfm footnote  


Curve Name  Curve Shape  A  B  P  K  Tr  Q 
US (U1)  Moderately Inverse  0.0226  0.0104  0.02  0  1.08  2 
US (U2)  Inverse  0.180  5.95  2  0  5.95  2 
US (U3)  Very Inverse  0.0963  3.88  2  0  3.88  2 
US (U4)  Extremely Inverse  0.0352  5.67  2  0  5.67  2 
US (U5)  Shorttime Inverse  0.00262  0.00342  0.02  0  0.323  2 
IEC (C1)  Standard Inverse  0  0.14  0.02  0  13.5  2 
IEC (C2)  Very Inverse  0  13.5  1  0  47.3  2 
IEC (C3)  Extremely Inverse  0  80  2  0  80  2 
IEC (C4)  Longtime Inverse  0  120  1  0  120  1 
IEC (C5)  Shorttime Inverse  0  0.05  0.04  0  4.85  2 
The following curve shows the U Series Inverse Curve Inverse Curve types.
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The next figure shows the C Series Inverse Curve types.
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Inverse Time Overcurrent Custom Curves
The custom curve settings for the 51 element have five levels of settings, using five data points. The resulting curve delimits the inversetime overcurrent operation characteristics using a linear interpolation method between the data points. This means that if an overcurrent scenario occurs and the current measurement is between Level 5 and Level 4, the time delay for such overcurrent level will be linearly calculated between the corresponding Time 5 and Time 4 settings. The pickup current values and delay times are all tunable parameters. The inverse time overcurrent characteristic of the 51 element is presented in the figure below.
NOTE: The custom curve only affects the trip time. Timed reset still follows the inverse curves and their parameters.
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Mask and Parameters
General Parameters
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Name  Description  Unit  Variable = {Possible Values}  

Pickup current  Pickup current for 51OC  pu or A  Ipck_51P_param = {[0, 30]}  
Time Dial  Time Dial Multiplier    TD51P_param = {[0, 600]}  
Reset type  Type of relay reset    Reset_set_param = {[0, 1]}  
Timed  Timed Reset  
Instant  Instantaneous Reset 
Inverse curve parameters
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Name  Description  Unit  Variable = {Possible Values}  

Inverse curve options  Option to use standard curve parameters or userdefined ones for inverse curves    User_coef_param = {[0, 1]}  
Use standard parameters for inverse curve  Standard inverse curves  
Use custom parameters for inverse curve  Userdefined inverse curves  
Standard IEC and US curve types  Curve types based on IEC or US Standard    curve_type_51P_param = {[0, 10]}  
U1  U.S. Moderately Inverse  
U2  U.S. Inverse  
U3  U.S. Very Inverse  
U4  U.S. Extremely Inverse  
U5  U.S. shorttime Inverse  
C1  IEC Class A Standard Inverse  
C2  IEC Class B Very Inverse  
C3  IEC Class C Extremely Inverse  
C4  IEC Longtime Inverse  
C5  IEC Shorttime Inverse  
Inverse curve with userspecific parameters  
Trip parameters  A  'A' characteristic for userdefined inverse curve    A_param = {[0, 200]} 
B  B' characteristic for userdefined inverse curve  B_param = {[0, 200]}  
P  'P' characteristic for userdefined inverse curve  P_param = {[eps, 2]}  
K  K' characteristic for userdefined inverse curve  K_param = {[0, 50]}  
Reset parameters  Tr  'Tr' characteristic for userdefined inverse curve    Tr_param = {[0, 50]} 
Q  'Q' characteristic for userdefined inverse curve  Q_param = {[eps, 50]} 
NOTE: Since P and Q are powers in the denominator, if they are 0, the denominator becomes 0 which means the equation becomes infinity. To prevent this situation, if the value is set to 0 by the user, it is not taken by the relay and instead epsilon, which is a very small value, is used by the relay.
Custom curve parameters
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Name  Description  Unit  Variable = {Possible Values}  

Use custom curves 51P  Option to use custom curves instead of standard time curves NOTE: The custom curve is only applicable to relay's trip time. Timed reset still follows the reset parameters in inverse curves tab.    cust51P_param = {0, 1}  
Level 1, 51P  The pickup current of Level 1 in 51P  pu/A  level1_51_param = { [0, 30] }  
Level 2, 51P  The pickup current of Level 2 in 51P  pu/A  level2_51_param = { [0, 30] }  
Level 3, 51P  The pickup current of Level 3 in 51P.  pu/A  level3_51_param = { [0, 30] }  
Level 4, 51P  The pickup current of Level 4 in 51P.  pu/A  level4_51_param = { [0, 30] }  
Level 5, 51P  The pickup current of Level 5 in 51P.  pu/A  level5_51_param = { [0, 30] }  
Time for level 1, 51P  The time delay for Level 1 in 51P.  s  time1_51_param = { [0, 600] }  
Time for level 2, 51P  The time delay for Level 2 in 51P.  s  time2_51_param = { [0, 600] }  
Time for level 3, 51P  The time delay for Level 3 in 51P.  s  time3_51_param = { [0, 600] }  
Time for level 4, 51P  The time delay for Level 4 in 51P.  s  time4_51_param = { [0, 600] }  
Time for level 5, 51P  The time delay for Level 5 in 51P.  s  time5_51_param = { [0, 600] } 
Inputs, Outputs and Signals Available for Monitoring
Inputs
Name  Description  Unit 

I  The per unit or actual RMS value (in A) of actuating current  pu or A 
Outputs
Name  Description  Unit 

Trip  The output of 51OC relay. By default, it is 0, if an overcurrent scenario is detected, it becomes 1. When the input signal falls below the pickup value, it resets.  Binary 
Sensors
Name  Description  Unit 

I  The per unit or actual RMS value (in A) of actuating current  pu or A 
Trip  The output of 51P overcurrent relay. By default it is 0, if an overcurrent scenario is detected, it becomes 1  Binary 
References
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Cfm footnotes display 
