1. Symmetrical Components (Fortescue)

Analyzing unbalanced faults (like Single Line-to-Ground) on a 3-phase system is mathematically difficult. We use Symmetrical Components to simplify it into three decoupled circuits:
Positive Sequence ($Z_1$): The normal balanced system (Source + Line + Trans). Determines 3-phase fault levels.
Negative Sequence ($Z_2$): Similar to $Z_1$ for static equipment, but different for motors/generators.
Zero Sequence ($Z_0$): The path for ground current. Heavily influenced by transformer grounding (NGR) and cable sheaths.

2. The Critical X/R Ratio

The fault current is not just determined by impedance magnitude ($Z$), but by the ratio of Reactance ($X$) to Resistance ($R$).
A high X/R ratio (e.g., > 10 near transformers/generators) means the fault is highly inductive. This causes a massive DC Offset, making the initial peak current ($i_p$) much higher than the RMS symmetrical value. Circuit breakers must be rated to withstand this peak mechanical force.

3. Fault Types & Severity

• 3-Phase Bolted Fault: All three phases shorted together. Usually the highest current (unless $Z_0$ is very low). Used for breaker sizing. Formula: $I_{3ph} = V_{ln} / Z_1$.
• Single Line-to-Ground (SLG): One phase to ground. Most common fault. Current depends on Grounding. Formula: $I_{slg} = 3 V_{ln} / (Z_1 + Z_2 + Z_0)$. Can exceed 3-phase fault if generator is solidly grounded!
• Line-to-Line (LL): Two phases shorted. Approx 87% of 3-phase fault.

4. Motor Contribution

When a fault occurs, induction motors act as generators for a few cycles, feeding current back into the fault. This increases the momentary "Make" current the breaker must handle. The calculator adds this contribution ($I_{motor} \approx 4-6 \times FLA$) to the total fault level.

5. Peak (Making) vs. Breaking Current

Peak (Making) Current ($i_p$): The absolute maximum instantaneous value (kA peak) occurring in the first half-cycle. Breakers must latch against the magnetic forces generated by this current.
Breaking Current ($I_b$): The RMS current flowing when the breaker contacts actually separate (e.g., 50ms later). The DC component has decayed partially. This determines the thermal/arc quenching rating.