PW-A1 · Three-phase AC

Three-phase connections: Y and Δ

A balanced three-phase source becomes either a Y connection or a delta (Δ) connection depending on how the same three coils are joined. Get a feel for the fact that the two connections are not different sources but two ways of wiring the same three EMFs.

Add the three EMFs to get 0

The three phasors turn together at the same speed, and the red arrow is their sum. Switch the phase spacing with the tabs and find the spacing at which the sum disappears.

The three tabs change the phase spacing. The faint dashed line is the path made by joining the three arrows head to tail, and its end is the tip of the red sum arrow.

Magnitude of the sum of the three EMFs

|E_a + E_b + E_c| ≈ 0.00 E

Exactly 120 degrees, so the three EMFs spread evenly like a star and their sum is 0. That is why closing the delta loop drives no circulating current.

Δ loop safe · Y neutral steady

Balanced · sum 0 ·

Y connection · joined at one point

Gather one end of each of the three coils (a, b, c) at a single point, and that common point becomes the neutral N, while the three other ends go out as the lines. When both source and load are balanced, the three currents flowing into the neutral also add to 0, so the neutral point's potential stays put even without a neutral wire. When the load is uneven this sum is left over, which is why places with uneven loads, such as distribution networks, run a neutral wire along.

Δ connection · closed into a loop

Join the end of each coil to the start of the next: the end of a to the start of b, the end of b to the start of c, and the end of c to the start of a, so the three coils form a closed triangular loop with no neutral point. The moment the loop closes, the three EMFs add in series around it, so their sum must be 0 for no circulating current to flow. In real generators and transformers the 3rd-harmonic voltages are in phase in all three phases and do not add to 0, so they circulate inside the Δ loop and do not appear on the lines outside.

Why the sum is 0

Seen as arrows in a plane, the three EMFs have equal length and point 120 degrees apart. Adding the horizontal parts together and the vertical parts together cancels both exactly, which is the same as the faint dashed line in the figure: joined head to tail, the arrows close an equilateral triangle and return to the starting point. This is why the neutral current of a Y is 0 and why the delta loop can be closed safely.

ObserveRe = 1 − ½ − ½ = 0

The real parts add to 0.

ChooseIm = 0 − √3/2 + ? = 0

The imaginary parts also add to 0.

Fill inE_a + E_b + E_c = ?

So the sum of the three EMFs is 0.

On your ownI_N = I_a + I_b + I_c = ?

For the same reason, the neutral current of a balanced Y is 0.

Back to the first screen

The red sum arrow vanished when the phase spacing was exactly 120 degrees. Gather that balanced set at one point and it is a Y connection; close it in a loop and it is a delta (Δ) connection, and the two are not different sources but two ways of wiring the same three EMFs. The single fact that the sum is 0 steadies the neutral point in a Y and keeps circulating current out of the loop in a delta.

A balanced three-phase set is three EMFs of equal magnitude spaced 120 degrees apart, and the three EMFs sum to 0. Tying one end of each to a common point gives the Y (star) connection, which has a neutral point; joining end to start in a loop gives the Δ (delta) connection, which has no circulating current because the sum is 0. The two are two wirings of the same three sources.

The next step

With the balanced set in hand, the next unit (PW-A2) works out how the connection shows up in voltage and current. In a Y the line voltage is √3 times the phase voltage, and in a delta the line current is √3 times the phase current; that √3 comes from the difference of the two phasors added here.