# Details on the Overcurrent Model Functionality

The 50P and 50N elements are defined as instantaneous phase overcurrent element and instantaneous neutral overcurrent element, respectively, if the time delay is set to zero. When setting a non-zero time delay, the element is set as a definite-time overcurrent element. If and only if the measured current becomes larger than the pickup value for a longer duration than the preset time delay, an overcurrent situation is asserted and the relay sends a trip signal through 50P or 50N. Otherwise, the element's internal timer is reset and the relay does not trip.

The time delay and reset mechanism of the 51P and 51N elements are applied similarly.

A tripping signal is sent through 51P or 51N, if the measured current is above the pickup value for a longer duration than a delay time. Both the pickup value and delay time can either be set by the user (custom curves) or determined by the standardized time curves (IEC or US time curves).

If either of the 50P (each phase), 50N, 51P (each phase), and 51N send a tripping signal, the model trips.

50P and 51P modules use the phase current while the operating quantity of 50N and 51N is the zero sequence current which is calculated as the following:

LaTeX Math Block |
---|

I_0 = \frac{1}{3} (I_a + I_b + I_c) |

## Inverse Time Curve Characteristics

### Inverse Time Overcurrent Curves Based on IEC and US Standards

By using a time dial multiplier (TD) and choosing the curve type, the operating and tripping time of the relay can be determined. Setting the multiplier to zero results in instantaneous response to all current levels. The pickup level for 51P and 51N is in per unit. If overcurrent is above the pickup level and custom curves are not being used, then the tripping time is calculated based on this equation.

*T = TD * [a + b/(I/I _{pickup})^{c}-1]*

**Equation 1: Trip Time Calculation**

The parameters shown in **Equation 1** differ based on the curve type. This model has 5 curve types from the US standard and 5 from the IEC standard as shown in the table below. The US standard coefficients are based on the values used by SEL relays [1] and it follows the IEEE C37.112-2018 equation. The IEC curves use the same equation and coefficients stated by the IEC 60255 standard for inverse time overcurrent relays.

Curve Name | Curve Shape | a | b | c |
---|---|---|---|---|

US (U1) | Moderately Inverse | 0.0226 | 0.0104 | 0.02 |

US (U2) | Inverse | 0.180 | 5.95 | 2 |

US (U3) | Very Inverse | 0.0963 | 3.88 | 2 |

US (U4) | Extremely Inverse | 0.0352 | 5.67 | 2 |

US (U5) | Short-time Inverse | 0.00262 | 0.00342 | 0.02 |

IEC (C1) | Standard Inverse | 0 | 0.14 | 0.02 |

IEC (C2) | Very Inverse | 0 | 13.5 | 1 |

IEC (C3) | Extremely Inverse | 0 | 80 | 2 |

IEC (C4) | Long-time Inverse | 0 | 120 | 1 |

IEC (C5) | Short-time Inverse | 0 | 0.05 | 0.04 |

The following curve shows the U Series Inverse Curve types.

The next figure shows the C Series Inverse Curve types.

## Inverse Time Overcurrent Custom Curves

The custom curve settings for 51X elements have five levels of settings, using five data points. The resulting curve delimits the inverse-time 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 51P or 51N element is presented in the figure below.

# Mask and Parameters

## General parameters

Name | Unit | Description |
---|---|---|

Frequency | Hz | The frequency of the measured current signals. Both 50 and 60 Hz are supported within the model. |

Base current | A | Base value for current |

Sample Time | s | Block sample time |

## Definite-time phase 50P

Name | Unit | Description |
---|---|---|

Enable 50P | - | Enable/disable definite-time phase overcurrenet element. |

Pickup current in 50P relay | pu | The pickup current in 50P element. |

Delay time in 50P relay | s | The time delay in 50P element. |

## Inverse-time phase 51P

Name | Unit | Description | |
---|---|---|---|

Enable 51P | - | Enable/disable inverse-time phase overcurrenet element. | |

Pickup current 51P | pu | The pickup current in 51P element. | |

Time Dial | - | Time Dial Multiplier | |

Curve types | - | Curve types based on IEC or US Standard | |

U1 | U.S. Moderately Inverse | ||

U2 | U.S. Inverse | ||

U3 | U.S. Very Inverse | ||

U4 | U.S. Extremely Inverse | ||

U5 | U.S. short-time Inverse | ||

C1 | IEC Class A Standard Inverse | ||

C2 | IEC Class B Very Inverse | ||

C3 | IEC Class C Extremely Inverse | ||

C4 | IEC Long-time Inverse | ||

C5 | IEC Short-time Inverse | ||

Customized curve | - | Choice to use custom curves instead of standard time curves | |

Pickup current | pu | Level 1 | The pickup current of Level 1 in 51P customized curve |

Level 2 | The pickup current of Level 2 in 51P customized curve | ||

Level 3 | The pickup current of Level 3 in 51P customized curve | ||

Level 4 | The pickup current of Level 4 in 51P customized curve | ||

Level 5 | The pickup current of Level 5 in 51P customized curve | ||

Pickup time | s | Time for level 1 | The time delay for Level 1 in 51P customized curve |

Time for level 2 | The time delay for Level 2 in 51P customized curve | ||

Time for level 3 | The time delay for Level 3 in 51P customized curve | ||

Time for level 4 | The time delay for Level 4 in 51P customized curve | ||

Time for level 5 | The time delay for Level 5 in 51P customized curve |

## Definite-time neutral 50N

Name | Unit | Description |
---|---|---|

Enable 50N | - | Enable/disable definite-time neutral overcurrenet element. |

Pickup current in 50N relay | pu | The pickup current in 50N element. |

Delay time in 50N relay | s | The time delay in 50N element. |

## Inverse-time neutral 51N

Name | Unit | Description | |
---|---|---|---|

Enable 51N | - | Enable/disable inverse-time neutral overcurrenet element. | |

Pickup current 51N | pu | The pickup current in 51N element. | |

Time Dial | - | Time Dial Multiplier | |

Curve types | - | Curve types based on IEC or US Standard | |

U1 | U.S. Moderately Inverse | ||

U2 | U.S. Inverse | ||

U3 | U.S. Very Inverse | ||

U4 | U.S. Extremely Inverse | ||

U5 | U.S. short-time Inverse | ||

C1 | IEC Class A Standard Inverse | ||

C2 | IEC Class B Very Inverse | ||

C3 | IEC Class C Extremely Inverse | ||

C4 | IEC Long-time Inverse | ||

C5 | IEC Short-time Inverse | ||

Customized curve | - | Choice to use custom curves instead of standard time curves | |

Pickup current | pu | Level 1 | The pickup current of Level 1 in 51N customized curve |

Level 2 | The pickup current of Level 2 in 51N customized curve | ||

Level 3 | The pickup current of Level 3 in 51N customized curve | ||

Level 4 | The pickup current of Level 4 in 51N customized curve | ||

Level 5 | The pickup current of Level 5 in 51N customized curve | ||

Pickup time | s | Time for level 1 | The time delay for Level 1 in 51N customized curve |

Time for level 2 | The time delay for Level 2 in 51N customized curve | ||

Time for level 3 | The time delay for Level 3 in 51N customized curve | ||

Time for level 4 | The time delay for Level 4 in 51N customized curve | ||

Time for level 5 | The time delay for Level 5 in 51N customized curve |

# Inputs and Outputs

## Inputs

Name | Description |
---|---|

I_{abc} | Three-phase currents |

Reset | The reset signal for the relay. The relay will be reset when this signal becomes 1. |

## Outputs

Name | Description | |
---|---|---|

Trip | The output of overcurrent relay. By default, it is 0, if an overcurrent scenario is detected, it becomes 1. | |

m | The output is a vector of 4 signals, to monitor the response of each protection element. | |

_50P | A three-dimension output of 50P, in the order of phase A, B, C | |

_51P | A three-dimension output of 51P, in the order of phase A, B, C | |

_50N | Output of 50N | |

_51N | Output of 51N |

References

SEL-451-5 Protection, Automation, and Bay Control System Instruction Manual