Protection Curve Analysis Based on IEC 60255 Standard

Online Overcurrent Relay Curve Analysis Tool (IEC 60255)

This online engineering tool is designed for overcurrent relay curve analysis (ANSI 50/51) and thermal relay modeling (ANSI 49). It accurately calculates the relay operating time according to IEC 60255, simulates trip behavior, and analyzes time–current characteristics.

Using this protection curve analyzer, you can simulate the real behavior of protection relays under overcurrent and overload conditions, and optimize TMS and pickup current settings for proper coordination.

1. Overcurrent Protection Calculation (ANSI 51)

Overcurrent relays utilize inverse-time characteristics to ensure selective and reliable equipment protection. This Engineering Calculator computes the relay operation for any given time instant ($t_i$​) and current ($I_1$​) using the following standard formula:

$$t_{relay} = TMS \times \left( \frac{A}{(I_{ratio})^p – 1} + B \right)$$

Where $I_{ratio}$​ represents the ratio of the actual primary current to the relay pickup current:

$$I_{ratio} = \frac{I_1}{I_{pickup}}$$

Digital Integration and Trip Simulation

This tool acts as a digital numerical simulator, replicating the logic of modern digital relays. It does not merely perform a static calculation; instead, it functions as a digital integrator. When the current exceeds the pickup threshold, the relay begins the process of “time accumulation.”

At each time interval ($\Delta t$), the tool calculates the following ratio:

$$\frac{\Delta t}{t_{relay}}$$

This value represents the “percentage of trip time accumulated” during that specific time step. Once the cumulative sum (the integral) reaches $1$(or $100\%$), the relay issues a trip command. This methodology accurately mimics the real-world performance of numerical relays in complex power system protection schemes.

2. Thermal Calculations (Thermal Model – ANSI 49)

The thermal model in this tool is designed based on IEC standards for overload protection. Unlike a relay with a fixed time, the thermal model operates on stored energy:

Thermal Capacity

This tool treats the equipment’s temperature or thermal capacity as a “tank.”

• If the current is below the rated current, the tank cools toward equilibrium.
• If the current is above the rated current, the tank heats up.

Thermal Model Formula

The equipment temperature rise is modeled using a first-order differential equation:

$$\theta_{new} = \theta_{prev} \times e^{-\Delta t/\tau} + (I / I_{base})^2 \times (1 – e^{-\Delta t/\tau})$$

• θ (theta): Thermal capacity (percentage).
• τ(tau / Time Constant): The parameter $T_{hot}$​ (heating time) or $T_{cold}$​ (cooling time), which determines the speed of the equipment’s thermal response.
• Initial Thermal Capacity: A critical input. In reality, equipment does not always start from zero temperature (e.g., a motor that operated recently remains warm). This input allows for analysis from a realistic starting point (e.g., 40% initial heat).

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How to use this tool? (Step-by-Step Guide)

1. Define Basic Settings:

• $I_{pickup}$​: The current above which the relay starts the countdown to trip.
• TMS: Time Multiplier Setting (used to shift the curve along the time axis).
• $I_{base}$​: Reference current for thermal calculations (usually the rated current of the motor or transformer).
• $T_{hot} / T_{cold}$: Thermal time constants of the equipment (obtained from the device datasheet).

2. Enter the Current Scenario:

In the table, enter the time intervals ($t$) and the currents ($I_1$​) corresponding to those moments.

• Example: If the current is $5A$ for $10$seconds, add a row with $t = 10$ and $I_1 = 5$​.

3. Analyze the Output:

• Trip Status: Check the final column of the table. If it reaches $100\%$, the device has tripped.
• Thermal Capacity: Review the thermal graph. If the curve approaches the red line ($100\%$), the equipment is at risk of thermal damage, even if the relay has not tripped.
• Charts: The Time-Current chart displays where the applied current falls within the relay’s operating curve.

Technical Note: This tool acts as a numerical simulator. Using smaller time steps ($\Delta t$)—for example, $1$second instead of $10$seconds—will significantly increase the accuracy of the integral and thermal calculations.