In an ideal power system, currents flow smoothly through balanced three-phase lines. But reality isn't ideal. A fault is any abnormal connection, like a tree branch hitting a power line or insulation failure. These events create a low-impedance path, causing a surge of current that can damage equipment if not cleared quickly.

Faults fall into two main categories.

Unsymmetrical faults are far more common. These affect one or two phases. They include:

• Single Line-to-Ground (SLG): One phase shorts to ground. This is the most frequent fault type.
• Line-to-Line (LL): Two phases short together.
• Double Line-to-Ground (DLG): Two phases short to each other and to ground.

Analysing these unbalanced conditions requires a more sophisticated tool, because standard circuit analysis assumes a balanced system.

To handle unsymmetrical faults, we use a powerful mathematical tool called the method of symmetrical components developed by Charles Fortescue in 1918. It allows us to break down any unbalanced three-phase system into three separate, balanced systems called sequence networks.

Each sequence network represents a different aspect of the fault:

• Positive-Sequence Network ($Z_1$): Represents the balanced, normal operating condition of the system. The currents are equal in magnitude and 120° apart, following the standard A-B-C phase rotation. This is the only network present during normal operation.

• Negative-Sequence Network ($Z_2$): Represents the reaction of the system to unbalance. These currents are also equal in magnitude and 120° apart, but they have the opposite phase rotation (A-C-B). Rotating machines like motors and generators have a much lower impedance to negative-sequence currents, which can cause severe overheating.

• Zero-Sequence Network ($Z_0$): Represents currents that are equal in magnitude and in phase with each other. These currents can only flow if there is a path to ground. In a balanced three-wire system, their sum is zero. But in a fault involving ground, the zero-sequence network provides the path for this ground current.

By connecting these sequence networks in different series and parallel combinations, we can model any type of fault and calculate the resulting fault currents for each phase. This gives protection engineers the precise data needed to set relays correctly.

Power systems contain multiple voltage levels connected by transformers. Calculating fault currents using actual volts, amps, and ohms across these transformers is tedious and error-prone. The Per-Unit (PU) system simplifies this by converting all values into dimensionless fractions of a common base value.

First, we establish base values for the system, typically a base MVA ($S_{base}$) and a base voltage ($V_{base}$). All other base quantities can be derived from these two.

Once we have our base values, we can convert any actual impedance into its per-unit equivalent.

If a component's impedance is given in per-unit on a different base, we must convert it to our new system base. This is a common task when combining data from different manufacturers.

While detailed PU calculations are essential for final relay settings, engineers often need a quick way to estimate fault levels in the field, especially during commissioning. The MVA Method is a popular shortcut for this.

This method treats impedances as inverse MVA ratings. The total short-circuit MVA at a point in the network is found by combining the MVA ratings of all sources contributing to the fault.

For example, consider a transformer with an impedance of 5% (0.05 pu) on a 10 MVA base, connected to a utility with a fault level of 500 MVA. To find the fault level on the secondary side of the transformer, we can treat them as two impedances in series.

1. Transformer MVA: $MVA_{TX} = \frac{10 \, MVA}{0.05} = 200 \, MVA$
2. Total MVA: Since the sources are in series, we add their reciprocals (like parallel resistors): $MVA_{total} = \frac{1}{\frac{1}{500} + \frac{1}{200}} = 142.8 \, MVA$

This 142.8 MVA is the fault level just downstream of the transformer. From here, you can calculate the bolted fault current and set your protection accordingly.

Understanding these methods—from symmetrical components to per-unit systems and the MVA shortcut—is crucial. They allow us to translate the complex dynamics of a power system into concrete numbers, which dictate the settings that keep the grid safe and reliable.