# Star and Delta connection

## STAR OR WYE (Y)-CONNECTED SYSTEM

This is the method of connecting the separate phases of a three-phase system. This system is obtained by joining together similar ends, either the start or the finish; the other ends are joined to the line wire. The common point N is called the neutral or star point, at which the similar ends are connected. The voltage between any line and the neutral point, i.e., the voltage across the phase winding, is called the phase voltage, and the voltage between any two outer lines is called the line voltage. The neutral point is connected to the earth.

pic sources: JB Gupta

The arrowheads on emfs and currents indicate the positive direction. Positive directions of emfs are taken from the star point outwards. The three phases are numbered as 1,2,3 or a,b,c or R, Y, B.usually, it is numbered as R, Y, B i.e the three natural colors red, yellow, and blue. There are mainly two phase sequences namely RYB and RBY. RYB is taken as positive and RBY as negative.

The emf induced in 3 phases is shown above. In star connection, there are two windings between each pair of outer, and due to the joining of similar ends together the emf induced in them are in opposition. The potential difference between the two outer known as line voltage, is the phasor difference of phases emfs of the two phases.

The potential difference between outer R and Y or the line voltage E RY is the phasor difference of phase emfs ER and

since the phase angle between phasors

From phasor diagram

similarly potential difference between outers Y and B or the line voltage

and potential difference between routers B and R or the line voltage

since in a star-connected system, each line conductor is connected to a separate phase, the current flowing through the lines and phases are the same.

3-phase power

phase voltages and currents in a balanced three-phase circuit is written as:

where ψ is the phase angle between phase voltage and phase current.

Total instantaneous power,

The sum of the three-second harmonic oscillating terms which have a progressive phase differences of 120 degrees is Zero. The instantaneous power in a 3-phase balanced system is constant and equal to three times the average power per phase.

Total power (p)=√3 *line voltage*power factor

Total apparent power

In a balanced star-connected system

• Line voltage is 120° apart.
• Line voltages are 30° ahead of the respective phase voltages.
• Line voltages are √3 times phase voltages.
• Line currents are equal to phase currents.
• The angle between line currents and the corresponding line voltages is(30° ±ψ);+ve for lagging currents and -ve for leading currents.

where cosψ is the angle between the respective phase current and phase voltage (not between line current and line voltage).

• In a balanced system, the potential of a neutral or star point is zero because potential at a neutral point or star point.

## MESH OR DELTA (Δ) connected system

From the above figure, when the starting end of one coil is connected to the finishing end of another coil, a delta connection is obtained. The directions of emfs in the coil have been taken as positive from start end to finish end. The current phasors are shown in the above figure:

Line currents

since the phase angle between phase current phasors I YR and -I BR is 60°,

The phase current in each winding is equal and let it be equal to Ip.

Line current

Similarly line current

since in a delta-connected system, only one phase is included between any pair of line outers,potential difference between the line outers, called line voltage and is equal to phase voltage.

i.e. Line voltage EL=phase voltage Ep

i.e Total power output=√3 *line current*power factor

Apparent power

Total reactive power, Q

In a balanced delta-connected system:

• Line currents are 120° apart.
• Line currents are 30° behind the respective phase currents.
• Line currents are √3 times phase currents.
• Line voltages are equal to phase voltages.
• The angle between line currents and the corresponding line voltages is(30° ±ψ);+ve for lagging currents and -ve for leading currents. same as in the star system.
• • where cosψ is the angle between the respective phase current and phase voltage(not between line current and line voltage).
• In a balanced system, the resultant emf in the closed circuit will be Zero.

There will be no circulating current in the mesh if no load is connected to the lines.

## Conversion of balanced load system from STAR TO DELTA AND VICE VERSA

Any balanced load system can be replaced by an equivalent delta-connected system or vice-versa because of the relationship between phase and line voltages and currents.

For example, a balanced star-connected load having an impedance of magnitude Z with a power factor cosψ in each phase can be replaced by an equivalent delta-connected load having an impedance of magnitude 3Z and power factor cosψ in each phase.