For the fault analysis in power system, symmetrical components are used because

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Option B: Sequence network do not have mutual coupling

Explanation & Concepts:
Symmetrical components (positive, negative, and zero sequence) are used in power system fault analysis because they decouple the unbalanced three-phase system into three independent single-phase sequence networks. This transformation eliminates the mutual coupling between the phases caused by transformers, transmission lines, and rotating machines, simplifying the calculation of unsymmetrical faults.

Working Principle: The transformation uses Fortescue’s theorem to map phase variables to sequence variables via the operator 'a' (where $a = 1\angle 120^{\circ}$). In the phase domain, the impedance matrix is dense and non-diagonal due to mutual coupling ($Z_{ab}, Z_{bc}, Z_{ca}$). By applying the symmetrical component transformation $V_{abc} = A V_{012}$, the system becomes diagonalized. This allows analysts to solve for currents and voltages in each sequence network independently, and then recombine them to find the actual phase values.

Key Formulas: $V_{abc} = A V_{012}$ — Transformation from sequence to phase components; $Z_{seq} = A^{-1} Z_{abc} A$ — Diagonalization of impedance matrix

Key Points: Symmetrical components represent an unbalanced system as the sum of three balanced systems.; Positive sequence components are present in all unsymmetrical faults.; Zero sequence currents only flow if there is a path to ground.; Sequence networks are completely independent (decoupled) in steady-state analysis.

Advantages: Simplifies complex unsymmetrical fault calculations; Allows use of Thevenin's equivalent for sequence circuits; Requires only one-third of the original system size for calculation

Disadvantages: Mathematically abstract compared to direct phase domain analysis; Requires conversion back to phase coordinates for final interpretation

Applications: Single line-to-ground (SLG) fault analysis; Line-to-line (LL) fault analysis; Double line-to-ground (LLG) fault analysis; Setting distance and differential protection relays

Additional Info: The transformation matrix $A = \begin{bmatrix} 1 & 1 & 1 \ 1 & a^2 & a \ 1 & a & a^2 \end{bmatrix}$ is used for the conversion.. Option A is incorrect because the result is not 'required' to be in symmetrical components; it is a means to an end. Option C is technically true as a side effect, but Option B is the fundamental physical reason why the method is computationally superior.

Answer: B is correct — Symmetrical components decouple the mutual impedances between phases, allowing sequence networks to be analyzed as independent, uncoupled circuits.

Exam Tip: Always remember that during an unsymmetrical fault, the positive, negative, and zero sequence networks are connected in different configurations (e.g., series for LG faults, parallel for LL faults) based on the fault boundary conditions.

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Option A: Results are required in terms of symmetrical components

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Option C: Number of equations becomes smaller

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Option D: All of above

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