Protecting equipment from the overcurrent is essential to system dependability and averting catastrophic breakdowns in modern electrical power systems. 

For successful protection coordination, relay working times must be accurately calculated since overcurrent relays activate when circuit current exceeds a predetermined threshold limit. 

The free online Time Overcurrent Relay Calculator lets electrical engineers immediately calculate relay operate times using IEEE and IEC curves.

What is a Time Overcurrent Relay?

Inverse Definite Minimum Time (IDMT) relays activate when current exceeds a predetermined pickup value with the operating time inversely related to current magnitude. 

Time overcurrent relays intentionally delay when overcurrent is detected, decreasing as fault current increases.

This inverse time characteristic has operational advantages. 

The relay isolates serious faults with high current magnitudes quickly. 

The relay provides greater time for moderate overloads minimizing nuisance tripping while protecting. 

Time overcurrent relays are ideal for coordinating numerous protective devices in series to operate the relay nearest to the fault first.

Time Overcurrent Relay Calculations

Time overcurrent relays respond quickly to faults because to their advanced time-current properties. The operating time varies on 

• Pickup current, 
• Clock dial setting, 
• Curve type & 
• Fault current magnitude. 

When load current exceeds pick up value, overcurrent relay works. These variables are related by mathematical formulas.

According to IEEE standards, the calculator supports 

• Moderately inverse (U1), 
• Inverse (U2), 
• Very inverse (U3), 
• Extremely inverse (U4), and 
• Short-time inverse (U5) relay curves. 

It also includes international IEC standard curves (C1-C5) for global electrical protection applications.

Important Calculation Variables

Pickup Current

The relay starts operating at this minimum current threshold. Pick-up current is the current transformer’s rated secondary current times the current setting. 

Proper pickup current selection keeps the relay from tripping during normal operation while being sensitive enough to identify faults.

Time Dial Setting

Adjusts relay operating time over its characteristic curve. US curves have time dial settings from 0.50 to 15.00, while IEC curves use 0.05 to 1.00.

Engineers can choose trip numerous relays using the time dial as a multiplier.

Plug Setting Multiplier (PSM)

PSM is the relay fault current to pickup current ratio. This dimensionless value shows overcurrent severity and affects relay response time via the inverse time-current characteristic.

Formulas 

Current setting, actual current & curve type constants determine relay operation time according to the International Electrotechnical Commission’s mathematical formula. 

The typical IEC equation is: 

t = TMS x [k / ((I/I_p)^α – 1)]

Where:

t – Operating time in seconds

TMS – Adjustable Time Multiplier (0.025–1.5)

k – Inverse characteristic curve constant k

α – Curve exponent defining inverse degree

I – Actual fault current in amps

I_p – Pickup current in amps

Characteristic type affects curve constants:

Standard Inverse: k = 0.14, α = 0.02

Very Inverse: k = 13.5, α = 1.0

Extremely Inverse: k = 80, α = 2.0

Inverse Long Time: k = 120, α = 1.0

These standardized curves allow relay performance to be predictable across manufacturers and permit advanced protection scheme coordination analysis.

Standards

• IEC 60255
• IEEE C37.112

Advantages 

The Time Overcurrent Relay Calculator automates complex logarithmic formulas and reduces human error. 

To enhance protection coordination, engineers can rapidly analyze curve selections, time dial settings & pickup values.

For global essential safety applications, all calculations follow IEEE and IEC standards for accuracy and dependability.

Applications

Many electrical engineering applications require time overcurrent relay calculations. 

Protection coordination analyses require exact operating time calculations to trip just the nearest relay to a malfunction, preventing power losses to healthy system components. 

Fault detection, coordination & system stability prevent equipment damage and downtime with proper relay settings.

These calculations prevent motors, transformers, and feeders from overload and short-circuit damage in industrial installations. 

Coordinated overcurrent protection protects radial lines and backups distance (or) differential protection in transmission and distribution networks.