Line Voltage, Phase Voltage, and Line Current: Explained Simply

If you’re diving into the world of 3-phase electrical systems, one of the first things you’ll hear about is the relationship between line voltage, phase voltage, and line current. It can be a little confusing at first, especially with different configurations like Wye (Y) and Delta (Δ) systems. But don’t worry—we’re going to walk through this step by step in plain English and back it up with some real examples.

Why Three-Phase Systems?

Before we get into the voltage and current stuff, here’s why we use three-phase power:

• It delivers constant power (not pulsating like single-phase)
• It’s more efficient for motors and heavy loads
• You can get more power with less conductor material

And to make it all work, we have to connect loads and generators in either Wye or Delta configurations. These configurations determine how voltages and currents behave in the system.

Wye (Y) Configuration

In a Wye system, each load or generator winding is connected between a line conductor and a neutral point.

So, you have:

• 3 line voltages: between the lines (e.g., L1-L2, L2-L3, L3-L1)
• 3 phase voltages: between each line and the neutral

Here’s the relationship:

Line Voltage (V_L) and Phase Voltage (V_P):

Line Current (I_L) and Phase Current (I_P): IL=IPI_L = I_P

In Wye, the line current is the same as the phase current.

Delta (Δ) Configuration

In a Delta system, each winding is connected between two lines. There’s no neutral.

• The phase voltage is the same as the line voltage:

• But the line current is √3 times the phase current:

In Delta, line current is not equal to phase current—it’s larger by a factor of √3.

A Quick Summary Table

Let’s Work Through Some Examples

Now that you’ve got the formulas, let’s use them in practice. Below are three example problems, each a bit more challenging than the last.

🟢 Beginner Example

Problem:
You have a Wye-connected motor supplied with a phase voltage of 230V. What is the line voltage?

Solution:

In Wye:

Answer: Line voltage ≈ 398.36V

🟡 Intermediate Example

Problem:
A Delta-connected load has a line current of 10 A. What is the phase current?

Solution:

In Delta:

Answer: Phase current ≈ 5.77 A

🔴 Advanced Example

Problem:
A Wye-connected balanced load consumes 15 kW at 400V line voltage and power factor of 0.9 (lagging). What is the line current?

Solution:

First, use the 3-phase power formula:

Answer: Line current ≈ 24.05 A

Common Misunderstandings

1. Line and phase voltage are always equal – False in Wye.
2. Phase current is always equal to line current – False in Delta.
3. You can calculate power with just one voltage and current – Not in 3-phase. Use the full 3-phase power formula:

Why This Matters

Whether you’re designing a power system, working on motors, or just trying to understand industrial equipment specs, knowing the difference between line and phase quantities is crucial. Misunderstanding them can lead to:

• Wrong cable sizing
• Equipment underperformance
• Incorrect circuit protection

And all of that can be costly—or even dangerous.

Final Thoughts

Three-phase systems aren’t magic. Once you know the geometry behind them (literally triangles!), the math makes sense. Just remember which configuration you’re working with—Wye or Delta—and apply the formulas accordingly.

And don’t forget: power = √3 × line voltage × line current × power factor. It’s the heartbeat of industrial electricity.

If you’re serious about electrical design or troubleshooting, this is foundational knowledge you absolutely need.

Powering Up with Delta and Wye: What You Need to Know