Overcurrent and Earth fault Relay setting Calculation Excel

IDMT (Inverse Definite Minimum Time) Overcurrent and Earth Fault Relay Calculation

1. Introduction

An IDMT relay is designed to protect electrical systems from overcurrent and earth faults. The operating time of an IDMT relay is inversely proportional to the magnitude of the fault current, meaning the higher the fault current, the faster the relay operates. These relays are commonly used in power systems to ensure that faults are isolated quickly to protect equipment and prevent system instability.

In general, an IDMT relay provides two types of protection:

• Overcurrent Protection (O/C): Protects the system against excessive current that exceeds the predetermined threshold, typically caused by short circuits or overloads.
• Earth Fault Protection (E/F): Protects the system when current flows to the ground due to insulation failure or grounding issues.

2. Operating Principle of IDMT Relay

The relay's operating time is given by the following equation, as per IEC or IEEE standards:

$T = \frac{K}{\left( \frac{I_{f}}{I_s} \right)^n - 1} \times TMS$

Where:

• T = Relay operating time (seconds)
• K = Constant based on relay characteristics (for standard inverse: K=0.14, for very inverse: K=13.5, for extremely inverse: K=80)
• I_f = Fault current (amps)
• I_s = Relay pick-up current or plug setting (amps)
• n = Constant based on the relay type (for standard inverse: n=0.02, for very inverse: n=1, for extremely inverse: n=2)
• TMS = Time Multiplier Setting, which adjusts the relay’s operating time

3. Overcurrent Protection (O/C) Calculation

For overcurrent protection, the relay is set to operate when the current exceeds a certain value, known as the plug setting. The calculation for relay operation can be broken down into the following steps:

1. Determine the relay's pick-up current (I_s): The pick-up current is determined by the plug setting multiplier (PSM) applied to the current transformer (CT) ratio. The plug setting is typically a percentage (e.g., 100%, 150%) of the rated CT current.

   $$I_s = PS \times I_{CT}$$

   Where:

   • PS = Plug setting (in percentage)
   • I_{CT} = CT secondary current (typically 1A or 5A)

2. Calculate the fault current (I_f): The fault current is the actual current measured by the relay during a fault condition.

3. Calculate the plug setting multiplier (PSM): The plug setting multiplier is the ratio of fault current to the pick-up current.

   $$PSM = \frac{I_f}{I_s}$$

4. Calculate the relay operating time: Based on the type of IDMT curve selected (standard inverse, very inverse, or extremely inverse), use the relay operating equation mentioned earlier.

4. Earth Fault Protection (E/F) Calculation

The earth fault relay protects against ground faults, which may occur due to insulation failures or direct contact between the live conductor and the earth. The calculation steps are similar to those for overcurrent protection, but typically the fault current is lower in magnitude.

1. Determine the pick-up current (I_s): For earth fault relays, the pick-up current is generally lower than for overcurrent relays, as earth faults often produce smaller currents.

2. Calculate the earth fault current (I_f): Measure or estimate the current that flows through the earth during a fault.

3. Calculate the plug setting multiplier (PSM):

   $$PSM = \frac{I_f}{I_s}$$

4. Calculate the relay operating time: Use the same formula as for overcurrent protection, adjusting based on the selected curve characteristics.

5. Time Multiplier Setting (TMS)

The TMS is a scaling factor that adjusts the relay's operating time. A lower TMS results in faster relay operation, while a higher TMS delays the tripping time. The value of TMS is chosen based on system coordination requirements to ensure selectivity among multiple relays.

6. Relay Coordination

Relay coordination ensures that the nearest relay to the fault operates first, while upstream relays provide backup protection. This requires careful setting of TMS and plug settings to achieve proper time discrimination between relays on different protection zones.

7. Example Calculation

Let’s assume a relay with the following parameters:

• Plug setting: 125% of 5A CT secondary (I_s = 6.25A)
• Fault current: 20A
• Time multiplier setting: 0.1
• Relay type: Standard inverse (K = 0.14, n = 0.02)

1. Calculate the PSM:

   $$PSM = \frac{20A}{6.25A} = 3.2$$

2. Calculate the operating time:

   $$T = \frac{0.14}{(3.2^{0.02} - 1)} \times 0.1 = 0.98 \text{ seconds}$$

In this example, the relay will operate in approximately 0.98 seconds.

8. Conclusion

IDMT overcurrent and earth fault relays provide reliable protection by operating inversely with respect to fault current. Their calculation involves setting appropriate values for pick-up current, fault current, PSM, and TMS to ensure proper relay operation and coordination with other protective devices in the system.

IDMT Low Over Current Relay Calculation

IDMT (Inverse Definite Minimum Time) low overcurrent relays are widely used for protecting power systems from overcurrent conditions, especially in distribution networks. These relays operate inversely to the magnitude of the fault current — higher fault currents result in shorter operating times, while lower fault currents lead to longer operating times. The IDMT characteristic ensures selective coordination between relays in a system, avoiding unnecessary tripping and allowing for safe fault clearance.

Key Concepts in IDMT Relay Calculation

1. Pickup Current (Ip): The pickup current is the minimum current that causes the relay to start timing. It is set as a multiple of the rated current and is typically denoted as Ip.

2. Time Multiplier Setting (TMS): The TMS adjusts the operating time of the relay. A lower TMS results in faster relay operation, while a higher TMS makes it slower. The operating time is directly proportional to the TMS.

3. Fault Current (If): This is the actual current seen by the relay during a fault condition. The operating time of the relay depends on the ratio of fault current to pickup current (If/Ip).

4. IDMT Characteristic Curves: Several IDMT relay characteristics are used based on different applications, such as:

   • Normal Inverse (NI)
   • Very Inverse (VI)
   • Extremely Inverse (EI)

   Each of these characteristics defines how quickly the relay operates in response to overcurrent.

General Formula for IDMT Relay Time Calculation

The operating time for an IDMT relay is given by the following equation (for a Normal Inverse characteristic):

$$t = TMS \times \frac{{k}}{{\left( \frac{{I_f}}{{I_p}} \right)^n - 1}}$$

Where:

• t: Relay operating time
• TMS: Time multiplier setting
• If: Fault current
• Ip: Pickup current
• k and n: Constants that depend on the type of IDMT curve.

Typical values of k and n for different characteristics are:

Characteristic	k	n
Normal Inverse	0.14	0.02
Very Inverse	13.5	1
Extremely Inverse	80	2

Steps for IDMT Relay Calculation

1. Determine the Pickup Current (Ip): The pickup current is generally set as a multiple of the full load current (or rated current) of the system. For example, if the full load current is 100A and the relay is set with a pickup of 1.5, then the pickup current is:

   $$I_p = 1.5 \times 100 = 150A$$

2. Determine the Fault Current (If): The fault current is usually calculated from the short-circuit analysis of the system or from protective coordination studies. Let's assume the fault current is 600A.

3. Calculate the Time Multiplier Setting (TMS): The TMS is chosen based on coordination studies with other protection devices in the system. Suppose the TMS is set to 0.2.

4. Select the IDMT Characteristic: Based on the protection scheme, choose the appropriate IDMT characteristic. Assume we are using the Normal Inverse characteristic with constants $k = 0.14$ and $n = 0.02$.

5. Calculate the Operating Time (t):

   Using the formula:

   $$t = TMS \times \frac{{0.14}}{{\left( \frac{{I_f}}{{I_p}} \right)^{0.02} - 1}}$$

   Substituting the values:

   $$t = 0.2 \times \frac{{0.14}}{{\left( \frac{{600}}{{150}} \right)^{0.02} - 1}}$$

   Simplifying:

   $$t = 0.2 \times \frac{{0.14}}{{(4)^{0.02} - 1}}$$ $$t = 0.2 \times \frac{{0.14}}{{1.029 - 1}} = 0.2 \times \frac{{0.14}}{{0.029}} = 0.2 \times 4.83$$ $$t \approx 0.97 \text{ seconds}$$

Thus, the relay will operate in approximately 0.97 seconds under this fault condition.

Practical Considerations

• Coordination: Relays at different locations on the network must coordinate to ensure that only the relay nearest to the fault trips first. This is done by adjusting TMS and pickup settings.
• CT Ratio: The relay is often connected via a current transformer (CT), and its settings need to account for the CT ratio.
• Verification: It’s important to verify the operating times for different fault levels to ensure proper coordination with other protective devices.

Conclusion

The calculation of an IDMT relay’s operating time involves determining the pickup current, fault current, TMS, and selecting the appropriate IDMT characteristic. These factors are then plugged into the IDMT equation to find the operating time. Proper coordination and setting of the relay are crucial for ensuring system protection and stability.

IDMT (Inverse Definite Minimum Time) Overcurrent Relay Calculation

An IDMT Overcurrent Relay is a protective device used in electrical power systems to detect overcurrent conditions. The operation of this relay is inversely proportional to the magnitude of the current — as the current increases, the relay operates faster. The "definite minimum time" refers to the minimum operating time for very high overcurrents.

Key Components of IDMT Relay Calculation

1. Pickup Current (Ip):
   The relay is set to operate when the current exceeds a preset value, called the pickup current. This is typically a multiple of the full load current or based on the rating of the protected equipment.

2. Time Multiplier Setting (TMS):
   The TMS is used to adjust the operating time of the relay. It is a multiplier applied to the basic inverse time characteristic. Lower TMS values will cause the relay to trip faster, while higher TMS values delay the operation.

3. Plug Setting Multiplier (PSM):
   The PSM is the ratio of the actual fault current to the pickup current of the relay.

   $$PSM = \frac{\text{Fault Current}}{\text{Pickup Current}}$$

   It represents how far the fault current is from the threshold set by the relay.

4. Time-Current Characteristic:
   The IDMT relay operates based on predefined time-current characteristics, such as:

   • Standard Inverse (SI)
   • Very Inverse (VI)
   • Extremely Inverse (EI) Each characteristic provides a different trip time based on the fault current and TMS. The general formula for calculating the operating time of the relay is:
   $$t = TMS \times \frac{k}{\left( PSM^n - 1 \right)}$$

   where:

   • $t$ = Operating time of the relay
   • $TMS$ = Time Multiplier Setting
   • $PSM$ = Plug Setting Multiplier
   • $k$ and $n$ are constants based on the selected curve (SI, VI, EI):
     • Standard Inverse (SI): $k = 0.14$, $n = 0.02$
     • Very Inverse (VI): $k = 13.5$, $n = 1.0$
     • Extremely Inverse (EI): $k = 80$, $n = 2.0$

Example Calculation

Let's say we have the following data:

• Pickup Current (Ip): 200 A
• Fault Current (If): 600 A
• TMS: 0.1
• Relay characteristic: Standard Inverse

1. Calculate PSM:

   $$PSM = \frac{If}{Ip} = \frac{600}{200} = 3$$

2. Using the formula for Standard Inverse characteristic:

   $$t = TMS \times \frac{0.14}{(PSM^{0.02} - 1)}$$

   Substituting values:

   $$t = 0.1 \times \frac{0.14}{(3^{0.02} - 1)} = 0.1 \times \frac{0.14}{1.023 - 1} = 0.1 \times \frac{0.14}{0.023} \approx 0.61 \, \text{seconds}$$

In this example, the relay will trip in approximately 0.61 seconds.

Key Points:

• The IDMT relay operates faster with higher fault currents due to its inverse characteristic.
• The choice of TMS and characteristic curve affects the overall protection scheme. A proper relay coordination study ensures that the relay settings provide optimal protection without causing unnecessary outages.

Applications:

IDMT overcurrent relays are used for:

• Feeder Protection
• Transformer Protection
• Motor Protection
• Generator Protection

IDMT Earth Fault Relay Calculation

Inverse Definite Minimum Time (IDMT) Relays are protective devices used in power systems to detect and clear faults, such as overcurrent and earth faults (also known as ground faults). The IDMT relay operates based on both the magnitude of fault current and the time delay before tripping. The relay's time delay is inversely proportional to the fault current, meaning the higher the current, the shorter the operating time. The relay also has a definite minimum time below which it will not operate, hence the name "Inverse Definite Minimum Time."

Earth Fault Relay Operation

An earth fault occurs when the live conductor makes contact with the ground or any grounded component, causing a flow of fault current to the earth. IDMT relays are specifically designed to detect such faults and initiate the opening of the circuit to isolate the faulty section of the system.

Key Parameters for Earth Fault Relay

1. Pickup Current (I_pickup): This is the minimum current required to activate the relay. It is typically set as a percentage of the full load current (e.g., 20% to 40%) depending on the system design and sensitivity requirements.

2. Time Multiplier Setting (TMS): This setting controls the time delay before the relay operates. The time multiplier scales the operation time of the relay, allowing adjustments to the protection scheme. Lower TMS means faster tripping.

3. Current-Time Characteristic: IDMT relays follow predefined current-time curves, which define the relationship between the fault current magnitude and the relay tripping time. The common curves are:

   • Normal Inverse
   • Very Inverse
   • Extremely Inverse These curves are used to coordinate the relay's operation with other protective devices.

4. Fault Current (I_fault): This is the magnitude of current during a fault condition. The relay detects this fault current and calculates the appropriate time delay before tripping.

IDMT Relay Time Equation

The tripping time for an IDMT relay is governed by the following equation:

$$t = TMS \times \left( \frac{k}{\left( \frac{I_{fault}}{I_{pickup}} \right)^n - 1} \right)$$