Relay Setting Calculator

Enter CT ratings, plug setting, time multiplier, fault current, and IEC curve type to calculate pickup current, PSM, and relay operating time.

Created by Luis GonzalezLast updated: May 9, 2026

How to Use This Calculator

1
Enter CT Primary Current (A)
Input the rated primary current of the Current Transformer (CT), typically ranging from 50A to 5000A.
2
Specify CT Secondary Current (A)
Provide the rated secondary current of the CT, which is usually 1A or 5A.
3
Input Plug Setting (Per-Unit)
Enter the pickup multiplier applied to the CT primary current, typically between 0.5 and 2.0. This sets the relay's sensitivity.
4
Enter Time Multiplier (TMS)
Input the time multiplier setting, which scales the relay's operating time curve. A higher TMS means slower operation for coordination.
5
Specify Fault Current (Primary) (A)
Provide the prospective fault current on the primary side of the CT. This is the current the relay would see during a fault condition.
6
Select IEC Curve Type
Choose the desired Inverse Time-Current Characteristic (TCC) curve type (Standard Inverse, Very Inverse, Extremely Inverse, or Long-Time Inverse).
7
Review your results
The calculator will display the relay's operating time, pickup current, plug setting multiplier (PSM), and CT ratio.

Example Calculation

An electrical engineer is setting a protective relay for a system with a 100A primary, 5A secondary CT. The plug setting is 1.0, TMS is 0.3, and a 2,000A primary fault current is expected, using a Standard Inverse curve.

CT Primary Current (A)

100

CT Secondary Current (A)

Plug Setting (Per-Unit)

1.0

Time Multiplier (TMS)

0.3

Fault Current (Primary) (A)

2,000

IEC Curve Type (select)

Standard Inverse (SI)

Results

0.700 s

Tips

Verify CT Ratio Accuracy

Ensure your Current Transformer (CT) ratio is correctly defined. An incorrect ratio will lead to miscalculated secondary currents, causing the relay to operate at the wrong fault levels or times, compromising system protection.

Balance Sensitivity and Selectivity

Adjust the Plug Setting (PS) and Time Multiplier (TMS) to achieve both sensitivity (tripping on actual faults) and selectivity (only the closest relay trips). A PSM below 1 means the relay won't operate, while a very low TMS can lead to nuisance trips.

Understand Inverse Time Characteristics

IEC inverse curves (Standard, Very, Extremely) mean the relay operates faster for higher fault currents. Choose the curve that best matches your system's coordination requirements and fault characteristics. Long-Time Inverse curves are often used for thermal protection.

Calculating Relay Settings for Electrical System Protection

This Relay Setting Calculator is an essential tool for electrical engineers, technicians, and protection specialists. It precisely calculates pickup current, Plug Setting Multiplier (PSM), CT ratio, and IEC inverse relay operating time for various curves (Standard, Very, Extremely, and Long-Time Inverse). Accurate relay settings are paramount for ensuring the safety, reliability, and selective coordination of power systems, adhering to critical standards like those set by the IEEE or IEC.

Why Accurate Relay Settings are Vital for Power System Reliability

Accurate relay settings are not merely technical adjustments; they are the backbone of power system reliability and safety. Improper settings can lead to catastrophic consequences, such as widespread blackouts (lack of selective coordination), severe equipment damage (delayed tripping), or unnecessary disruptions (nuisance tripping). In complex electrical grids, protective relays must operate precisely within milliseconds to isolate faults, preventing them from cascading and ensuring that only the affected section is de-energized. This precision protects expensive assets like transformers and generators, safeguards personnel, and maintains continuity of supply to critical loads, underscoring their irreplaceable role in modern electrical infrastructure.

The Inverse Time-Current Logic of Protective Relays

The Relay Setting Calculator is based on the inverse time-current characteristics defined by IEC (International Electrotechnical Commission) standards. These characteristics ensure that the relay operates faster for higher fault currents, providing quicker protection for more severe faults.

The core calculations involve:

CT Ratio: CT Ratio = CT Primary Current / CT Secondary Current
Pickup Current: Pickup Current = CT Primary Current × Plug Setting
Plug Setting Multiplier (PSM): PSM = Fault Current (Primary) / Pickup Current
IEC Operating Time (T):
```
T = (K × TMS) / ((PSM)^alpha - 1)
```
Where K and alpha are constants specific to the chosen IEC curve type (e.g., for Standard Inverse, K=0.14, alpha=0.02).

This intricate logic ensures that relays respond appropriately to varying fault magnitudes while allowing for coordination with other protective devices.

💡 To accurately model the behavior of complex electrical networks, our Node Voltage Method Calculator can help analyze voltage potentials at various points.

Worked Example: Setting a Standard Inverse Relay

An electrical engineer needs to configure a protective relay. The current transformer (CT) has a primary current rating of 100A and a secondary current of 5A. The relay's plug setting is 1.0 per-unit, and the time multiplier setting (TMS) is 0.3. A prospective fault current of 2,000A (primary) is anticipated, and a Standard Inverse (SI) curve is selected.

Here's the step-by-step calculation:

Calculate CT Ratio: 100A / 5A = 20.
Calculate Pickup Current: 100A × 1.0 = 100A.
Calculate Plug Setting Multiplier (PSM): 2,000A / 100A = 20.
Calculate Operating Time (Standard Inverse): For SI, K=0.14 and alpha=0.02. T = (0.14 × 0.3) / (20^0.02 - 1) T = 0.042 / (1.0600 - 1) T = 0.042 / 0.0600 = 0.700 seconds.

The relay will operate in 0.700 seconds under these fault conditions.

💡 For analyzing current distribution in parallel circuits during fault conditions, our Mutual Inductance Calculator (oops, wrong link) is not relevant here. Ah, from the list: /calculators/noise-figure-calculator -> Noise Figure Calculator. Still not great. I need to pick two most topically relevant ones. The provided list is: - /calculators/mppt-vs-pwm-charge-controller-calculator -> MPPT vs PWM Charge Controller Calculator - /calculators/mutual-inductance-calculator -> Mutual Inductance Calculator - /calculators/node-voltage-method-calculator -> Node Voltage Method Calculator - /calculators/noise-figure-calculator -> Noise Figure Calculator - /calculators/norton-equivalent-circuit-calculator -> Norton Equivalent Circuit Calculator Okay, "Node Voltage Method Calculator" is about circuit analysis, which is relevant to understanding the flow of current and voltage that protective relays monitor. "Norton Equivalent Circuit Calculator" is also about circuit simplification and analysis. These are the best two from the list. To analyze the steady-state behavior of complex electrical circuits where relays are integrated, our Norton Equivalent Circuit Calculator can simplify network analysis.

Principles of Overcurrent Protection in Power Systems

Overcurrent relays are fundamental components in protecting electrical grids and industrial facilities from a wide range of faults, from short circuits to overloads. The primary goal is selective coordination, a design principle ensuring that only the smallest section of the power system affected by a fault is isolated, leaving the rest of the system operational. This prevents widespread outages and minimizes disruption. Protection engineers often refer to standards like IEEE Std 242 (Buff Book) or IEC 60255 series, which provide guidelines for the application and testing of protective relays. For instance, a typical coordination scheme might aim to clear a fault within 0.1 to 0.5 seconds at the nearest protective device, allowing upstream devices to act as backup with slightly longer delays (e.g., 0.3 to 0.5 seconds of time grading).

Interpreting Relay Trip Times for System Coordination

Protection engineers interpret relay operating times in the context of comprehensive system coordination studies, often visualized through time-current characteristic (TCC) curves. These curves plot the operating time of various protective devices (fuses, circuit breakers, and relays) against fault current magnitudes. The goal is to ensure that for any fault, the device closest to the fault trips first, with a sufficient time margin (typically 0.2 to 0.4 seconds) before the next upstream device operates. This "time grading" prevents unnecessary outages. For example, a fast trip time of 0.1 seconds might be desired for a feeder breaker to protect a critical load, while a main substation breaker might have a slower trip time of 0.5 seconds to provide backup protection. Analyzing these curves helps identify potential coordination gaps or overlaps that could compromise system reliability, ensuring that faults are isolated effectively within milliseconds to seconds.

Frequently Asked Questions

What is a protective relay in electrical power systems?

A protective relay is an electrical device designed to detect abnormal operating conditions in an electrical power system, such as overcurrents, overvoltages, or underfrequency, and then initiate a trip command to a circuit breaker to isolate the faulty section. Its primary role is to protect equipment from damage, ensure system stability, and maintain the safety of personnel by rapidly clearing faults.

What is the Plug Setting Multiplier (PSM) for a protective relay?

The Plug Setting Multiplier (PSM) is a critical parameter for inverse time overcurrent relays, representing the ratio of the actual fault current to the relay's pickup current. A PSM greater than 1 indicates that the fault current exceeds the relay's set threshold, causing it to operate. A higher PSM means a more severe fault, and for inverse curves, the relay will operate faster.

What is the Time Multiplier Setting (TMS) in relay coordination?

The Time Multiplier Setting (TMS) is a factor used to scale the operating time of an inverse time overcurrent relay, allowing engineers to adjust the relay's trip time without changing its sensitivity (pickup current). By varying the TMS, protection engineers can achieve selective coordination, ensuring that in a fault condition, the closest upstream protective device operates first, minimizing disruption to the power system.

What are IEC inverse time-current characteristics (TCC) curves?

IEC inverse time-current characteristics (TCC) curves define the relationship between the magnitude of a fault current and the operating time of an overcurrent relay. These curves (Standard, Very, Extremely, Long-Time Inverse) ensure that the relay operates faster for higher fault currents. Each curve has a distinct shape and is chosen based on the specific protection requirements and coordination needs within a power system, like protecting transformers or cables.