PW-A1 · Three-phase AC

Three-phase connections: Y and Δ

A balanced three-phase source becomes Y or delta (Δ) depending on how you join the same three parts. Build the intuition that both are just two wirings of the same three EMFs.

Add the three EMFs down to zero

Three phasors spin together at the same speed. Change the phase spacing until their sum (the red arrow) vanishes.

Tap to switch the phase spacing.

Magnitude of the sum of the three EMFs

|E_a + E_b + E_c| ≈ 0.00 E

Exactly 120 degrees. The three EMFs balance like a star and the sum is zero. Closing the delta loop draws no circulating current.

Δ loop safe · Y neutral steady

Balanced · sum 0 ·

Y connection · joined at one point

Tie one end of all three coils (a, b, c) to a single point. That common point is the neutral N. The other three ends run outward as the lines. When balanced, the currents arriving at the neutral also sum to zero, so the potential holds steady even with no neutral wire.

Δ connection · closed into a loop

Connect the end of each coil to the start of the next: a-end to b-start, b-end to c-start, c-end to a-start. The three coils form a closed triangle loop. There is no neutral. The instant the loop closes, the three EMFs add in series around it, and only if that sum is zero does no circulating current flow.

Why the sum is zero

Picture the three EMFs as arrows on a plane: equal length, fanned out 120 degrees apart. Add the horizontal components together and the vertical components together, and each side cancels exactly. This is why the neutral-wire current in Y is zero, and why the delta loop can be closed safely.

ObserveRe = 1 − ½ − ½ = 0

The real parts sum to zero.

ChooseIm = 0 − √3/2 + ? = 0

The imaginary parts sum to zero too.

Fill inE_a + E_b + E_c = ?

So the three EMFs sum to zero.

On your ownI_N = I_a + I_b + I_c = ?

For the same reason the neutral-wire current of a balanced Y is zero.

Back to the first screen

The red sum arrow vanished exactly when the spacing was 120 degrees. Gather that balanced set at one point and you get Y; close it into a loop and you get the delta (Δ) connection. The two are not different sources but two ways of joining the same three EMFs, and the single fact that they sum to zero guarantees both the steady Y neutral and the safety of the delta loop at once.

A balanced three-phase set is three EMFs of equal magnitude spaced 120 degrees apart. Their sum is zero. Tie one end to a common point and you get the Y (star) connection — a neutral appears. Join end to start around a loop and you get the Δ (delta) connection — the sum is zero, so no circulating current. The two are two wirings of the same three sources.

The next step

With the same balanced set in hand, the next unit (PW-A2) shows how the connection appears in voltage and current. In Y the line voltage is √3 times the phase voltage; in delta the line current is √3 times the phase current. That √3 comes straight from the difference of two of the phasors you added here.