Prasun Barua

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How to Calculate Short Circuit Current for LV and MV Systems

Learn step-by-step how to calculate LV and MV short circuit currents with examples and FAQs.


Short circuit current calculation is a fundamental aspect of electrical engineering, essential for ensuring the safety, reliability, and protection of power systems. Both low-voltage (LV) and medium-voltage (MV) systems require accurate short circuit analysis to select proper protective devices, determine fault levels, and design equipment that can withstand short-term currents.

This article provides a precise, step-by-step guide on calculating short circuit currents for LV and MV systems, with examples and frequently asked questions (FAQs) to clarify common doubts.

1. Understanding Short Circuit Currents

A short circuit occurs when an unintended low-resistance path is formed between two points of different potential, allowing excessive current to flow. This current is much higher than normal operating current and can cause equipment damage, fire, and safety hazards.

Short circuit currents are categorized as:

  • Symmetrical short circuit current (\(I_k\)): Steady-state rms value after transient decay.
  • Peak short circuit current (\(I_p\)): Maximum instantaneous value during the initial moments of a fault.
  • Initial short circuit current (\(I_{k''}\)): Current immediately after the short circuit occurs.

Calculating these currents is vital for:

  • Correct selection of circuit breakers, fuses, and protective relays.
  • Determining mechanical and thermal stresses on equipment.
  • Compliance with electrical standards (IEC, IEEE, NEC).

2. Short Circuit Calculation Principles

Short circuit currents depend on:

  • System Voltage – Higher voltages generally produce higher short circuit currents.
  • Source Impedance – The impedance of generators, transformers, and upstream networks limits the fault current.
  • Fault Location – The closer the fault to the source, the higher the current.
  • Type of System – LV (up to 1 kV) and MV (1 kV – 36 kV) systems differ in impedance, configuration, and protection schemes.

The general formula for calculating three-phase short circuit current at a point in the system is:

\[ I_{sc} = \frac{U_{LL}}{\sqrt{3} \cdot Z_{eq}} \]

Where:

  • \(I_{sc}\) = short circuit current (A)
  • \(U_{LL}\) = line-to-line voltage (V)
  • \(Z_{eq}\) = equivalent impedance seen from the fault point (Ω)

For single-phase faults, the formula is:

\[ I_{sc} = \frac{U_{LN}}{Z_{eq}} \]

Where \(U_{LN}\) is the line-to-neutral voltage.

3. Step-by-Step Calculation for LV Systems

Example: Consider a 400 V, 3-phase LV system supplied from a transformer with a rated power of 500 kVA and 5% impedance.

Step 1: Identify system parameters

  • Transformer rated voltage: 400 V (line-to-line)
  • Transformer rated power: 500 kVA
  • Transformer impedance: 5% (0.05 pu)

Step 2: Calculate transformer base impedance

\[ Z_{base} = \frac{U_{LL}^2}{S_{rated}} \]

\[ Z_{base} = \frac{(400)^2}{500,000} = 0.32\ \Omega \]

Step 3: Calculate transformer short circuit impedance

\[ Z_{sc} = Z_{base} \cdot \frac{Z_{\%}}{100} \]

\[ Z_{sc} = 0.32 \cdot 0.05 = 0.016\ \Omega \]

Step 4: Calculate short circuit current

\[ I_{sc} = \frac{U_{LL}}{\sqrt{3} \cdot Z_{sc}} \]

\[ I_{sc} = \frac{400}{\sqrt{3} \cdot 0.016} \approx 14,434\ A \]

Result: The three-phase short circuit current is approximately 14.4 kA.

4. Step-by-Step Calculation for MV Systems

Example: Consider a 11 kV MV system supplied by a 5 MVA transformer with 10% impedance.

Step 1: Identify system parameters

  • Transformer voltage: 11 kV
  • Transformer power: 5 MVA
  • Transformer impedance: 10%

Step 2: Calculate base impedance

\[ Z_{base} = \frac{U_{LL}^2}{S_{rated}} \]

\[ Z_{base} = \frac{(11,000)^2}{5,000,000} = 24.2\ \Omega \]

Step 3: Calculate short circuit impedance

\[ Z_{sc} = Z_{base} \cdot \frac{Z_{\%}}{100} \]

\[ Z_{sc} = 24.2 \cdot 0.10 = 2.42\ \Omega \]

Step 4: Calculate short circuit current

\[ I_{sc} = \frac{U_{LL}}{\sqrt{3} \cdot Z_{sc}} \]

\[ I_{sc} = \frac{11,000}{\sqrt{3} \cdot 2.42} \approx 2,619\ A \]

Result: The three-phase short circuit current is approximately 2.62 kA.

5. Important Considerations

  • Impedance of upstream network: For MV systems fed from a grid, include the source impedance.
  • Voltage correction: Consider the actual system voltage during operation.
  • Fault type: Single-line-to-ground, line-to-line, and double-line-to-ground faults have different current levels.
  • Standards compliance: IEC 60909 and IEEE 242 provide guidelines for LV/MV short circuit calculations.

6. Example of Short Circuit Calculation with Multiple Transformers

Scenario: Two 500 kVA, 11 kV/400 V transformers supply a bus. Each transformer has 5% impedance. Calculate the short circuit current at the LV bus.

  1. Calculate individual transformer LV short circuit impedance:

    \(Z_{sc} = Z_{base} \cdot \frac{Z_{\%}}{100} = 0.32 \cdot 0.05 = 0.016\ \Omega\)

  2. Equivalent impedance of parallel transformers:

    \(Z_{eq} = \frac{Z_{sc}}{2} = 0.008\ \Omega\)

  3. Short circuit current:

    \(I_{sc} = \frac{400}{\sqrt{3} \cdot 0.008} \approx 28,867\ A\)

Result: LV bus short circuit current doubles due to parallel transformers.

7. FAQs

Q1: What is the difference between LV and MV short circuit calculations?
A1: The methodology is similar, but LV systems typically have lower voltages and higher fault currents. MV systems involve additional factors like upstream network impedance, longer cables, and multiple transformers.

Q2: Why is per-unit (pu) system used in short circuit calculations?
A2: Per-unit simplifies calculations by normalizing voltage, current, and impedance, making it easier to handle multi-voltage systems and transformers.

Q3: Do cable impedances matter in LV short circuit calculations?
A3: Yes, especially for long cable runs, cable resistance and reactance reduce the fault current. Standards recommend including them for accurate calculations.

Q4: Can software be used for short circuit calculations?
A4: Yes. Tools like ETAP, SKM PowerTools, DIgSILENT PowerFactory, and MATLAB/Simulink can automate LV/MV short circuit analysis and provide detailed fault currents.

Q5: How to select circuit breakers based on short circuit current?
A5: Choose a breaker with a rated breaking capacity higher than the calculated short circuit current, ensuring safe interruption without damage.

8. Conclusion

Accurate calculation of short circuit currents in LV and MV systems is essential for designing safe and reliable electrical installations. By understanding system parameters, calculating impedances, and considering network configurations, engineers can select proper protective devices and ensure compliance with safety standards.

Key takeaways:

  • Use the basic formula \(I_{sc} = \frac{U_{LL}}{\sqrt{3} \cdot Z_{eq}}\) for three-phase faults.
  • Include all relevant impedances: transformers, cables, generators, and upstream network.
  • Apply per-unit system for multi-voltage networks to simplify calculations.
  • Verify results with standards (IEC 60909, IEEE) and consider software tools for complex systems.
Prasun Barua is an Engineer (Electrical & Electronic) and Member of the European Energy Centre (EEC). His first published book Green Planet is all about green technologies and science. His other published books are Solar PV System Design and Technology, Electricity from Renewable Energy, Tech Know Solar PV System, C Coding Practice, AI and Robotics Overview, Robotics and Artificial Intelligence, Know How Solar PV System, Know The Product, Solar PV Technology Overview, Home Appliances Overview, Tech Know Solar PV System, C Programming Practice, etc. These books are available at Google Books, Google Play, Amazon and other platforms.