Mathematics:
Va = V₀ + V₁ + V₂
Vb = V₀ + a²V₁ + aV₂
Vc = V₀ + aV₁ + a²V₂
where a = e^(j2π/3) = 120° rotation operator
What it shows: All phasors originate from the origin. This is the standard textbook representation showing how sequence components combine to form phase voltages.
Key insight: Va + Vb + Vc = 3V₀ (zero sequence appears tripled in the sum)
Mathematics:
V₁₂a = V₁ + V₂ (positive + negative sequence only)
V₁₂b = a²V₁ + aV₂
V₁₂c = aV₁ + a²V₂
Final: Va = V₀ + V₁₂a, Vb = V₀ + V₁₂b, Vc = V₀ + V₁₂c
What it shows: The V₁₂ components (containing only positive and negative sequence) rotate around the neutral shift V₀. This separates the "balanced" part (V₁₂) from the "unbalanced" part (V₀).
Key insight: V₀ represents the neutral-to-ground voltage shift that affects all phases equally.
Mathematics:
Same V₁₂ components as Column 2, but:
Va = Real(V₀) + V₁₂a
Vb = Real(V₀) + V₁₂b
Vc = Real(V₀) + V₁₂c
Real(V₀) slides along x-axis as V₀ rotates
What it shows: The same V₁₂ components now oscillate horizontally as they follow only the real component of the neutral shift. This creates a "sliding" reference frame.
Key insight: Shows how the neutral shift's real component affects the horizontal positioning of all phase voltages.
All three columns show the same phase voltages Va, Vb, Vc - just with different reference points and visualization methods.
The final result Va is identical in all cases - only the visualization and reference frame differ.
Each representation emphasizes different aspects of the same underlying physics.