An unbalanced system of three phase voltage having RYB sequence actually consists of

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Examoogle · Accepted Answer

Option D: All of above

Explanation & Concepts:
According to Fortescue's theorem, any unbalanced system of $n$ related phasors can be decomposed into $n$ sets of balanced phasors called symmetrical components. For a 3-phase system, this results in three sequence sets: positive, negative, and zero sequence components.

Working Principle: An unbalanced set of phasors $(V_R, V_Y, V_B)$ is transformed into symmetrical components $(V_0, V_1, V_2)$ using a linear transformation matrix. The positive sequence maintains the original phase sequence ($RYB$), the negative sequence has reversed sequence ($RBY$), and the zero sequence consists of three equal phasors in phase with each other.

Key Formulas: $V_0 = \frac{1}{3}(V_R + V_Y + V_B)$ — Zero sequence component; $V_1 = \frac{1}{3}(V_R + aV_Y + a^2V_B)$ — Positive sequence component; $V_2 = \frac{1}{3}(V_R + a^2V_Y + aV_B)$ — Negative sequence component

Key Points: Fortescue's Theorem states that $n$ unbalanced phasors yield $n$ symmetrical components.; The operator $a = 1 \angle 120^\circ$ is used to define phase shifts.; Positive sequence represents normal operating balanced conditions.; Negative sequence occurs during faults and unbalanced loading.; Zero sequence exists only if there is a path for return current (ground).

Advantages: Simplifies power system fault analysis significantly.; Allows independent analysis of sequence networks.

Disadvantages: Requires complex number calculation.; Assumes linear network components.

Applications: Protection relaying for ground faults.; Unbalanced load analysis in distribution networks.

Additional Info: If the system were perfectly balanced, $V_1$ would equal the phase voltage, while $V_0$ and $V_2$ would be zero.. The presence of all components characterizes general asymmetry in a 3-phase circuit.

Answer: D is correct — An unbalanced 3-phase system, by definition of symmetrical components, contains all three sets of sequence components (positive, negative, and zero) unless specific constraints on current or grounding exist.

Exam Tip: Always remember that in a 3-wire system (no neutral), the zero sequence component $V_0$ is zero because the sum of currents $I_R+I_Y+I_B=0$ must hold.

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Option A: A positive sequence component

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Option B: A negative sequence component

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Option C: A zero sequence component

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