Short Circuit Current Calculations

To calculate the short circuit current in a power system we use the basic formula Isc = V / Z where Isc represents short circuit current, V represents pre-fault voltage and Z represents total impedance. In this article we will explore about the short circuit current, steps to calculate short circuit current, and formulas to calculate short circuit current. We will also solve some examples related to the calculation of short circuit current. Let’s start learning on the topic “How to Calculate Short Circuit Current.”

What is a Short Circuit Current?

Short circuit current is the maximum amount of current that flows through a power system during the fault occurrence. The short circuit current depends on factors like voltage, total impedance and the type of fault. The short circuit current is represented by I_sc.

In other words, the current flowing at the time of the short circuit is called as the short circuit current.

Short Circuit Current

Basic Formula to Calculate Short Circuit Current

To calculate short circuit current we have different formulas according to different circuits.

General Formula to Calculate Short Circuit Current

The general formula to calculate the short circuit current is given by

Isc = V / Z

where,

Isc is short circuit current

V is the pre-fault voltage

Z is the total impedance

Short Circuit Current Formula for Generators

The short circuit current formula for the generators is given by

I_sc = Generator rated current / Impedance of the short circuit path

Short Circuit Current Formula for Transformers

The short circuit current formula for transformers is given by

I_sc = KVA rating of the source / Secondary side voltage of the transformer

Types of Faults

In power system various type of fault can occur such as

• Single Line-to-Ground (SLG) Fault: In this fault one phase gets connected to the ground. This type of fault has the highest impedance and results in the lowest short circuit current.
• Line-to-Line (LL) Fault: In an LL fault two phases are shorted to each other.
• Double Line-to-Ground (DLG) Fault: In this fault two phases are shorted to each other and to the ground.
• Three-Phase (3P) Fault: In a 3P fault all three phases are shorted to each other and to the ground.

Fault Analysis Methods

For examining short circuit currents in a power system different methods are used for analyzing. Some of the approach methods are per-unit method which does calculations by standardizing voltages, currents, and impedances to a common base value. Another methods is Symmetrical Components Method in which we break down an unbalanced three phase system into three balanced systems so that we can calculate short circuit currents for any type of fault. Also we have Direct Method which Calculates short circuit current directly from a basic formula using actual values of voltages and impedances.

How to Calculate Short Circuit Current

To calculate short circuit current first we analyze the circuit and check the components like it is a generator, transformer or circuit with different impedances. If the given element is generator, we calculate the short circuit current by dividing the generator rated current with the impedance present in the short circuit path. If the given element is transformer, then we calculate the short circuit current by dividing the KVA rating of the source by secondary side voltage of the transformer. If the impedances are given then, we use the general formula for calculating the short circuit current i.e., by dividing pre-fault voltage with total impedance.

Solved Examples on Short Circuit Current

There are some solved examples of calculate short circuit current given by direct method:

Example 1

Find the short circuit current given the pre-fault voltage is 40V and the total impedance is 5 Ohms.

Pre-fault Voltage = 40 V

Total Impedance = 5 ohms

The general formula of short circuit current is given by:

Isc = V / Z

Isc = 40 / 5

Isc = 8 A

The short circuit current is 8 A.

Example 2

If the secondary side voltage of the transformer is 6 V and KVA rating of the source is 30 then, calculate the short circuit current.

KVA rating of the source = 30

Secondary side voltage of the transformer = 6 V

The formula to calculate the short circuit current in transformers is given by:

I_sc = KVA rating of the source / Secondary side voltage of the transformer

I_sc = 30 / 6

I_sc = 5 A

The short circuit current is 5A.

Example 3

A generator has a generator rated current of 20 A and impedance in the short circuit path is 5 ohms then, find the short circuit current.

Generator rated current = 20 A

The impedance in the short circuit path = 5 ohms

The formula for calculating short circuit current in generators is given by:

I_sc = Generator rated current / Impedance of the short circuit path

I_sc = 20 / 5

I_sc = 4 A

The short circuit current is 4A.

Conclusion

From the above discussion we can conclude that the current flowing at the time of short circuit is called short circuit current. To calculate the short circuit current we have different formulas based on the elements in the circuit. The general formula to get the short circuit current is the ratio of pre-fault voltage to total impedance. To get the short circuit current for transformers we require the KVA rating of the source and secondary side voltage of the transformer. To get the short circuit current for generators we require the generator rated current and the impedance of the short circuit path.

How to Calculate Short Circuit Current – FAQs

What is the Formula for Short Circuit Current?

The basic formula for calculating the short circuit current is Isc = V / Z.

How Do You Measure Short Circuit Current?

The short circuit current is measured by connecting ammeter in series with the positive and negative terminals of the panel to each other.

What Causes Short Circuit Current?

The faulty insulations causes the short circuit current.