Star and Delta connection


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

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The arrow heads on emfs and currents indicate the positive direction.A positive directions of emfs are taken from star point outwards.The three phases is 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.

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The emf induced in 3 phases are shown above.In star connection there are two windings between each pair of outer and due to 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 phase angle between phasors

From phasor diagram

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

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

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

  • Line voltage are 120° apart.
  • Line voltages are 30° ahead of the respective phase voltages.
  • Line voltages are √3 times of 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 respective phase current and phase voltage(not between line current and line voltage).

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

MESH OR DELTA(Δ) connected system

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From the above figure,when the starting end of one coil is connected to the finishing end of another coil ,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 above figure:

Line currents

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

Assuming balanced load

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

Line current

Similarly line current

since in 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 balanced delta-connected system:

  • Line currents  are 120° apart.
  • Line currents  are 30° behind the respective phase currents.
  • Line currents are √3 times of 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 star system.
  • where cosψ is the angle between respective phase current and phase voltage(not between line current and line voltage).
  • In 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.

Comparison between STAR and DELTA systems

1Similar ends are joined together.Dissimilar ends are joined together.
2Phase voltage is equal to 1/ times the line voltage therefore star connected alternators needs a less number of turns per phase and less insulation .Hence 3-phase alternators are usually star-connected.Phase voltage is equal to line voltage
3Phase current is equal to line current i.e Ip=ILPhase current is equal to 1/ times line current
4Possible to carry neutral wire to the load. only star connected system can give 3-phase 4-wire arrangement. hence star connected system can be used for lightning as well as power load ie. for an unbalanced load.Not Possible to carry  neutral wire to the load.
5Neutral point of  a star-connected system can be connected to earth ,so relays and protective devices can be provided in star-connection system for protection of the system against the ground faults.
6 Delta connections are mostly used in transformer for operating small low voltage 3-phase motors and are suitable for rotary convertors.

Most of three phase induction motors are delta-connected.

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 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.

For a balanced star-connecetd load,


For the same line in delta-connected system values of voltage and current as in case of star-connected system


comparing (i) and (ii) we get,




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