Power Systems - Fault Analysis Complete Study Notes

Symmetrical Components

A three-phase system is said to be symmetrical when the system viewed from any phase is similar. Thus, in a three-phase symmetrical system the self-impedance of all the three phases are equal and the mutual impedances, if any between the three phases are the same any three phase system having unbalanced phasor quantities can be represented in terms of three phase balanced phasor components as a combination of positive, negative and zero sequence component, which are as follows

Positive Phase Sequence Components

It represents a set of balance phasors V_a1, V_b1 & V_c1 These components have three phasors equal in magnitude displaced by 120^o and having same phase sequence as original phasors.

Negative Phase Sequence Components

These components have three phasors V_a2, V_b2 & V_c2 equal in magnitude displaced by 120^o but having phase sequence opposite to original phasors. It represents a set of balanced phasors.

Zero Sequence Components

These phasors V_ao, V_bo & V_co are equal in magnitude and having zero phase displacement.

Sequence Impedance

The positive sequence impedance of an equipment is the impedance offered by the equipment to the flow of positive sequence current. similarly, the negative sequence or zero sequence impedance of the equipment is the impedance offered by the equipment to the flow of corresponding sequence current.

Sequence Impedance of a Transmission Line

Positive sequence impedance Z₁ = Z_s - Z_m

Negative sequence impedance Z₂ = Z_s - Z_m

Zero sequence impedance Z₀ = Z_s + 2Z_m + 3Z_n

where, Z_s = Self-impedance per phase

Z_m = Mutual impedances between phases

Most of the faults that occur on power systems are not the balanced (i.e., symmetrical) three-phase faults but the unbalanced (i.e., unsymmetrical) faults, like single line-to-ground (SLG) faults. The typical frequency of occurrence for the three-phase, SLG, line-to-line, and double line-to-ground (DLG) faults as 5%, 70%, 15%, and 10% respectively.

In general, the three-phase fault is considered to be the most severe one. However, it is possible that the SLG fault may be more severe than the three-phase fault under two circumstances:

(1) the generators involved in the fault have solidly grounded neutrals or low-impedance neutral impedances

(2) it occurs on the wye-grounded side of delta-wye-grounded transformer banks.

Single Line to Ground Fault:

In general, the SLG fault on a transmission system occurs when one conductor falls to ground or contacts the neutral wire.

Line to Line Fault:

In general, a line to line (L-L) fault on a transmission system occurs when two conductors are short circuited.

Double Line to Ground Fault:

In general, the Double Line to Ground fault on a transmission system occurs when two conductors fall and are connected through ground or when two conductors contact the neutral of a three-phase grounded system.

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