What is the relationship between line voltage and phase voltage in a star connection?

In a star (Y) connection, the line voltage is √3 times the phase voltage: V_L = √3 × V_ph. For example, if the phase voltage is 230 V, the line voltage is 230 × 1.732 = 400 V. The line current equals the phase current in a star connection.

How do you convert star impedance to delta impedance?

For a balanced 3-phase load, delta impedance equals 3 times the star impedance: Z_delta = 3 × Z_star. For example, if Z_star = 10 Ω, then Z_delta = 30 Ω. This conversion is essential for analyzing equivalent circuits in power systems.

What is the formula for 3-phase power in star and delta connections?

The total 3-phase power is the same for both connections: P = √3 × V_L × I_L × cos(φ), where V_L is line voltage, I_L is line current, and cos(φ) is the power factor. For a purely resistive load, cos(φ) = 1 and P = √3 × V_L × I_L.

Star-Delta (Y-Δ) Conversion

Y-Δ Transform • 3-Phase Circuits • Line & Phase Values • Power Factor — Simulate • Explore • Practice • Quiz

Mode

Configuration

Z Impedance (Ω) 100 Ω

Line Voltage (V) 400 V

Frequency

Show Conversion Equations Show Phasor Diagram

Line Voltage

400 V

Phase Voltage

231.0 V

Line Current

2.31 A

Phase Current

2.31 A

Total Power (3φ)

1600 W

Z Star

100 Ω

Z Delta

300 Ω

Power Factor

1.00

Understanding Star-Delta (Y-Δ) Conversion — Free Interactive 3-Phase Circuit Simulator

Star-delta conversion (also known as Y-Δ transformation) is a fundamental technique in electrical engineering for analyzing 3-phase circuits. In a star (Y) connection, three impedances share a common neutral point, while in a delta (Δ) connection, they form a closed triangle between the three line terminals. This simulator lets you toggle between both configurations and observe how line voltages, phase voltages, line currents, and phase currents change in real time. Understanding these relationships is essential for power distribution, motor starting, and industrial electrical systems.

Star (Y) Connection — Voltage and Current Relationships

In a star connection, each impedance is connected between a line terminal and the neutral point. The key relationships are: V_line = √3 × V_phase and I_line = I_phase. This means the line voltage is 1.732 times larger than the phase voltage, while the line current equals the phase current. Star connections are commonly used in power distribution because they provide access to two voltage levels (e.g., 230V phase and 400V line in European systems) and allow a neutral wire for single-phase loads.

Delta (Δ) Connection — Voltage and Current Relationships

In a delta connection, each impedance is connected between two line terminals, forming a triangle. The key relationships are: V_line = V_phase and I_line = √3 × I_phase. Here the phase voltage equals the full line voltage, but the line current is 1.732 times the phase current. Delta connections are widely used for motor windings and high-power loads because they can handle higher power without a neutral conductor.

Y-Δ Impedance Conversion

For balanced loads, converting between star and delta impedances is straightforward: Z_Δ = 3 × Z_Y. This means the delta impedance is always three times the star impedance for the same balanced load. The total 3-phase power remains identical regardless of connection type: P = √3 × V_L × I_L × cos(φ). This equivalence is the foundation of star-delta motor starters, which reduce starting current by initially connecting motor windings in star configuration before switching to delta for normal operation.

Who Uses This Simulator?

This simulator is designed for electrical engineering students, TVET trainees studying 3-phase power systems, industrial electricians learning about motor connections, and instructors teaching star-delta conversion theory. It provides visual, hands-on understanding of 3-phase circuit relationships without requiring laboratory equipment or physical motor starters.

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