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When a short circuit occurs in the power network, it can cause large currents that may lead to overheating or damage of electrical equipment. The voltage in the network can drop significantly, disrupting the normal operation of devices connected to it. To minimize the impact of such faults, it's essential to calculate the short-circuit current for proper selection of equipment, protection system design, and components that limit the current flow.

I. Calculation Conditions

  1. Infinite System Assumption: Assume the system has infinite capacity, meaning the bus voltage remains constant after a fault. This is valid when the calculated impedance is much larger than the system impedance. For 3~35kV power grids, systems above 110kV are considered infinite, and only the impedance of components below 35kV needs to be calculated.
  2. Reactance vs. Resistance: In high-voltage equipment, consider only reactance (X) of generators, transformers, and reactors. For overhead lines and cables, if resistance is more than one-third of reactance, both are considered; otherwise, only reactance is used.
  3. Three-Phase Short-Circuit Focus: Short-circuit calculations typically use three-phase faults because they produce the highest current. Equipment designed for three-phase faults can safely handle single- or two-phase faults as well.

II. Simplified Calculation Method

While detailed calculations can be complex, there’s a "mouth-style" method that simplifies the process. By remembering seven key points, you can estimate the short-circuit current without complex formulas. These include understanding reference values, standardizing parameters, and applying simple rules for different components like transformers, lines, and reactors.

Key Parameters:

  • Sd: Three-phase short-circuit capacity (MVA), used to check switch breaking capacity.
  • Id: RMS value of the periodic component of the short-circuit current (KA), used for checking breaking current and thermal stability.
  • IC: RMS value of the first cycle full current (KA), also known as impulse current, used for dynamic stability checks.
  • ic: Peak value of the first cycle full current (KA), used for dynamic stability checks.
  • X: Reactance (Ω).

The system short-circuit capacity (Sd) and the total reactance (X) at the fault point are the most important factors in the calculation.

III. Reference Values and Standardization

To simplify calculations, a reference capacity (Sjz = 100 MVA) and reference voltage (Ujz) are chosen. From these, the reference current for each voltage level can be derived using the formula S = √3 × U × I. For example, at 10.5 kV, the reference current is about 5.59 KA.

Each parameter (like voltage, current, and reactance) is converted into a per-unit value relative to the reference. This makes calculations easier and more standardized.

IV. Infinite System Short-Circuit Current Calculation

The formula for the short-circuit current in an infinite system is: I*d = 1 / X*, where X* is the total reactance in per-unit. Then, the actual RMS short-circuit current is: Id = Ijz × I*d. The inrush current (IC) is calculated as: IC = Id × √(1 + (KC - 1)^2), with KC = 1.8. For smaller transformers (≤1000 kVA), the impact coefficient is reduced to 1.3, resulting in lower inrush currents.

V. Practical Steps for Quick Calculations

Here’s a quick guide using simplified rules:

  1. System Reactance: If the system capacity is 100 MVA, its reactance is 1. If the capacity increases, the reactance decreases proportionally. For example, 200 MVA gives a reactance of 0.5.
  2. Transformer Reactance: Use coefficients like 10.5 for 110kV, 7 for 35kV, and 4.5 for 10kV. Divide the transformer capacity (in MVA) by these numbers to get the per-unit reactance.
  3. Reactor Reactance: For a reactor with 10% rated reactance, divide the percentage by the rated capacity (in MVA) and multiply by 0.9 for adjustment.
  4. Line and Cable Reactance: Overhead lines: 6kV = km, 10kV = 1/3, 35kV = 3%. Cables: 20% of overhead line values.
  5. Total Reactance: Add all per-unit reactances before the fault point. The short-circuit capacity is then 100 / X*.
  6. Short-Circuit Current: Use specific multipliers based on voltage level: 9.2 for 6kV, 5.5 for 10kV, 1.6 for 35kV, and 0.5 for 110kV.
  7. Inrush Current: For transformers under 1000 kVA, the inrush current is equal to the short-circuit current. For larger ones, it’s 1.5 times the short-circuit current, with a peak of 2.5 times.

By following these steps, even those without access to detailed manuals can quickly estimate the short-circuit current. The core idea is to understand the total reactance up to the fault point, including the system reactance. With practice, this method becomes second nature, helping engineers and technicians make informed decisions efficiently.

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