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Three-Phase Load Star-Delta Connection · Phase Voltage and Line Voltage Relationship

Same three-phase supply connected to loads in Star (Y) and Delta (Δ) configurations.
Side-by-side comparison of voltage relationships under both connections, verifying the \(\sqrt{3}\) proportionality.

Supply and Load Parameters

220 V
100 V400 V
50 Hz
40 Hz60 Hz
50 Ω
10 Ω200 Ω

Star (Y) Connection Parameters

Line Voltage \(V_{\text{line}}\) 380.6 V
Phase Current \(I_{\text{phase}}\) 4.40 A
Line Current \(I_{\text{line}}\) 4.40 A

\(V_{\text{line}} = \sqrt{3}\,V_{\text{phase}},\quad I_{\text{line}} = I_{\text{phase}}\)

Delta (Δ) Connection Parameters

Line Voltage \(V_{\text{line}}\) 380.6 V
Phase Current \(I_{\text{phase}}\) 7.61 A
Line Current \(I_{\text{line}}\) 13.18 A

\(V_{\text{line}} = V_{\text{phase}},\quad I_{\text{line}} = \sqrt{3}\,I_{\text{phase}}\)

Comparative Analysis

\(\displaystyle\frac{V_{\text{line,Y}}}{V_{\text{line,Δ}}}\) 1.000
\(\displaystyle\frac{I_{\text{line,Δ}}}{I_{\text{line,Y}}}\) 3.000

Under the same supply, Δ-connected load phase voltage is \(\sqrt{3}\) times that of Y-connected load;
Δ-connected line current is 3 times that of Y-connected load.

Star (Y) Connection · Voltage Waveforms

Phase A Phase B Phase C Line Voltage AB

Delta (Δ) Connection · Voltage Waveforms

AB Phase BC Phase CA Phase

Theoretical Basis

Y-connection: load bears phase voltage, line voltage is \(\sqrt{3}\) times phase voltage (\(\approx 1.732\)).
Δ-connection: load bears line voltage (equal to phase voltage), line current is \(\sqrt{3}\) times phase current.
Under the same supply, Δ-connected load has higher voltage and larger current.

Characteristic Interpretation

Y-connection is suitable for long-distance power distribution (with neutral point grounding); each phase load voltage is \(1/\sqrt{3}\) of the line voltage.
Δ-connection is suitable for high-power equipment such as motors, providing higher starting torque.
Total three-phase power is independent of connection type (for the same line voltage and line current).