Delta connection in power system is shown in the below diagram

As shown in the diagram of the three-phase Δ-connected motor, the three line conductors are brought from the three junctions of the delta and named R(U1&W2), Y (U2&V2), and B(W1&V1), and this connection is called a three-phase three-wire delta connected system.

the delta connection is also called a mesh connection because it forms a closed circuit.

This connection looks like the Greek letter Δ hence named as delta connection.

In Δ connection, only three phase three-wire system can be formed no neutral exists in delta connection.

In delta connected system only one phase is included between R&Y, Y&B, R&B any two lines hence magnitude of voltage between two-line voltages is equal to the phase voltage in a delta or mesh-connected system.

And the current flowing through phases is

IL= √3 IPH

Three line currents are equal in magnitude and displaced by 120 degree from each other.

**Voltage in balance delta connected system**

Relation between line voltage and phase voltage

As the system is balanced hence three-phase voltages are equal in magnitude and displaced by 120 degree apart from each other from the diagram of delta connection we can see that only one phase winding is included between any pair of lines hence phase voltage is equal to line voltage for mesh connection.

VL = VPH

### Relation between line current and phase current

As said, the above system is balanced the three currents flowing through the system are IR, IY, and IB are equal in magnitude and displaced by 120 degree.

Current in line 1 is I1 = IR – IB

Current in line 2 is I2 = IY – IR

Current in line 3 is I3 = IB – IY

**Line current IL= √3 Iph**

### Power in Delta Connection

IPH = IL /√3 ….. (From IL = √3 IPH)

VPH = VL

Putting these values in power in VPH x IPH x CosФ

P = 3 x VL x ( IL/√3) x CosФ

P = √3 x√3 x VL x ( IL/√3) x CosФ

P = √3 x VLx IL x CosФ

Hence proved;

Power in Δ Connection,

P = 3 x VPH x IPH x CosФ …. or

P = √3 x VL x IL x CosФ

### Advantages of delta connection

- This type of connection is most suitable for rotary conveyer
- The majority of 3 phase loads are delta connected rather than star connection
- Most three phase induction motors are delta connected