Week 4: Wye-Delta

                                           Wye-Delta

Three terminal networks are used in three phase connection, matching networks and electrical filters.

The Figure  shows Wye (Y) and Tee (T) networks

The Figure  shows delta (∆) and pie (Π) network.

            

Example: 

Delta to wye conversion

It is easy to work with wye network. If we get delta network, we convert it to wye to work easily. To obtain the equivalent resistance in the wye network from delta network we compare the two networks and we confirm that they are same. Now we will convert the 2nd figure  (a) delta network to the first figure (a) wye network.

From the 2nd figure  (a) for terminals 1 and 2 we get,

R₁₂ (∆) = R_b || (R_a + R_b)

From figure 2 (a) for terminals 1 and 2 we get,

R₁₂(Y) = R₁ + R₃

Setting wye and delta equal,

R₁₂(Y) = R₁₂ (∆) we get,

Equations (v), (vi) and (vii) are the equivalent resistances for transforming delta to wye conversion.



Wye to Delta conversion

Example:

Now we will solve a problem how to convert delta to wye network. It will give clear concept.

converting the delta network to wye network.

The equivalent Y network configuration is shown below.

For conversion to wye network to delta network adding equations (v), (vi) and (vii) we get,

 R₁R₂ + R₂R₃ + R₃R₁ = R_aR_bR_c(R_a +R_b + R_c)/(R_a + R_b + R_c)²

                                = R_aR_bR_c/(R_a + R_b + R_c) —————— (ix)

Dividing equation (ix) by each of the equations (v), (vi) and (vii) we get,

R_a = R₁R₂ + R₂R₃ + R₃R₁/ R₁

R_b = R₁R₂ + R₂R₃ + R₃R₁/ R₂

R_c = R₁R₂ + R₂R₃ + R₃R₁/ R₃

Learnings:

Learning to Identify what network it is to know what formula are we using; the wye-delta or delta-wye.