Star and Delta Connection

Star and delta connections are the types of three-phase circuits. Electric circuits are divided into Single-phase AC circuits and Three-phase AC circuits. A Single-phase system consists of two conductors, one is called phase (through which current flows) and the other is called neutral ( acts as a return way to complete the circuit). A Three-phase system consists of three conductors, which is the more economical way to transmit power than a single-phase system. In electrical circuit analysis there are certain type of complex circuits that have resistances connected in either series or parallel. These complex arrangements are usually connected in the T, Y, Delta or pi connections. Among these star and delta are some common types of connection.

Star Connection

Star connection is denoted by ‘ Y ‘. It is a 4-wire system and one of the type of Three-phase circuit. It consists of 3 phase wires and 1 neutral. There are two types of star connection, 4 –wire 3 – phase system (three-phase wires and one neutral wire) and 3 – wire 3 phase system (three-phase wires). Star Connections are mainly used for the Power Transmission Network for longer distances. This type of connections are required when there is need for a neutral point. It is mostly used in low and medium voltage distribution systems.

Star connection

Current and Voltages in Star Connection

The Common point of the Star Connection is called Neutral or Star Point. Consider V_R, V_B , V_Y are three phase voltages and V_RB, V_BY , V_RY are line voltages:

Current and Voltages in Star Connection

Now from the figure above,

|V_R|=|V_B|=|V_Y|=|V_Phase|

Let V_Phase= V_P,

|V_R|=|V_B|=|V_Y|=|V_P|

We can write V_RY as,

V_RY = V_R + (-V_Y)

V_RY = V_R -V_Y

To find the magnitude use parallelogram law of vectors,

[Tex]V_{RY}=\sqrt{V_R^{2}+V_Y^{2}+2V_RV_Y \cos 60^{\circ}}[/Tex]

we know that |V_R|=|V_B|=|V_Y|=|V_P|, V_RY=V_L (Line voltage)

and [Tex]\cos 60^{\circ}=\frac{1}{2}[/Tex],

Then,

[Tex]V_{L}=\sqrt{V_P^{2}+V_P^{2}+2V_PV_P\frac{1}{2}}[/Tex]

[Tex]V_{L}=\sqrt{V_P^{2}+V_P^{2}+V_P^{2}}[/Tex]

[Tex]\text{take}\ V_P^{2} \ \text{as common term}[/Tex]

[Tex]V_{L}=\sqrt{V_P^{2}(1+1+1)}[/Tex]

[Tex]V_{L}=\sqrt{3}V_P[/Tex]

• Line Voltage is equals to root three times the phase voltage, i.e,

V_L =√3 V_P

where V_L is line Voltage

V_P is Phase Voltage

From the circuit shown above in star connection line is in series with its phase winding,

I_R= I_B = I_Y = I_P

• Line Current is equals to Phase Current, i.e,

I_L = I_P

Where, I_L is line current

I_P is phase current.

Advantages of Star Connection

• Load: It has the ability to spread the load in between the phases. It is good for unbalanced loading.
• Voltage: It is used for high voltage.
• Turns: For the same voltage, star connection requires less number of turns than a delta connection because of induced emf of an alternator is directly proportional to number of turns.
• Use: Star Connection is used in both transmission and distribution networks. star connection is used for long distances since the insulation required is less.

Disadvantages of Star Connection

• Limitations in using cable length: Star connection should follow a particular distance between central switch and the nodes, there is signal degradation and issue in performance occurs when that distance exceeds.
• Time consuming: If there is any fault occurs then each and every connection must be checked for trouble shooting.
• Cost: If there is any need For upgrading the central switch then the cost increases.

Applications of Star Connection

• Used in Home and office Networks: A simple and Easy expandable network for Everyday used products like computers, printers are connected to a central switch. Small to medium sized offices uses star connection for their computer networks.
• Used in data centers: The servers and storage devices which are interconnected within the data centers use star connection as it provides the center switch for traffic management.
• Used in Industries: Industries use sensors, control devices which are communicated using this star connection that connects to the central switch.

Delta Connection

It is also called mesh connection. Delta connection is a 3- wire system and all the three wires are phases. No neutral wire in delta connection. Delta connection is denoted by Δ . Delta Connection is generally used in distribution networks. It is sometimes also in the shape of pi and mostly in shape of a triangle or can be referred to as delta. there is no common or neutral point available in the system. In this connection every wire is connected to two adjoining wires in the form of a triangle Δ, all three points form the three phases as shown below.

Delta Connection

Current and Voltages in Delta connection

Consider I_R , I_B , I_Y are the Line Currents and I_RB , I_BY , I_RY are the Phase Currents in Delta connection as shown below:

Current and Voltages in Delta Connection

From the above connection,

|I_RB|=|I_BY|=|I_RY|=|I_Phase|=|I_P|

From the above diagram we can write,

I_R = I_RB – I_RY

I_Y = I_RY – I_BY

I_R = I_BY – I_RB

Use the parallelogram law of vectors to find the magnitude,

[Tex]I_R = \sqrt{ I_{RB}^{2} + I_{RY}^{2}+2I_{RB}I_{RY} \cos 60^{\circ}}[/Tex]

Use, [Tex]\cos 60^{\circ}=\frac{1}{2}[/Tex]

[Tex]I_R = \sqrt{ I_{P}^{2} + I_{P}^{2}+2I_{P}I_{P} \frac{1}{2}}[/Tex]

[Tex]I_R = \sqrt{ I_{P}^{2} + I_{P}^{2}+I_{P}^{2}}[/Tex]

[Tex]I_R = \sqrt{ I_{P}^{2}(1 + 1+1)}[/Tex]

[Tex]I_R = \sqrt{3 I_{P}^{2}}[/Tex]

[Tex]I_R = \sqrt{3} I_{P}[/Tex]

Neutral point does not exist in the delta connection the phase voltage and line voltage are equal,

V_RB = V_BY = V_RY = V_L (Line voltage)

• Line voltage is equal to the phase voltage,

V_L = V_P

where V_L is line Voltage

V_P is Phase Voltage

• Line Current is equals to root three times the phase Current, i.e,

I_L =√3 I_P

where I_L is line Current

I_P is Phase Current

Advantages of Delta Connection

• Convenient: Delta connection is simple and easier to make, so that it is easier for installation and maintenance.
• Cost: lesser cost and Protection is simple. As there is no neutral wire which is useful where a balanced system is desired.
• less current: For the same power output, less current per winding using a delta connection.
• Use: Delta Connection is generally used in distribution networks.

Disadvantages of Delta Connection

• No Neutral point: Neutral point exists if it is created artificially. Not having neutral wire is a disadvantage where there is need for the neutral point.
• Load Balancing: Load balancing in delta connection is difficult compared to Star connection.
• Single phase: Delta connection is not suitable for single phase load.

Applications of Delta Connection

• Used in Electric power: Delta connection distributes the power across households in residential areas over short distances.
• Torque: Delta Connections are used in applications which require high starting torque.
• Power generation system: used in three-phase generators where the generator windings are to be in a delta pattern and is common in some power generation systems.

Delta to Star Conversion

Consider three resistances R_AB, R_BC , R_CA are connected in delta to the terminals A,B,C as shown below:

Delta to Star Conversion

From the figure above,

Resistance between A and B for star connection = Resistance between A and B for delta connection

R_A + R_B = R_AB || (R_BC + R_CA)

For example,

[Tex]a||b=\frac{a}{a+b}[/Tex]

Then

[Tex]R_{A} + R_{B} = \frac{R_{AB} (R_{BC} + R_{CA})}{(R_{AB} +R_{BC} + R_{CA})}[/Tex] → (1)

Similarly,

[Tex]R_B + R_C =\frac{ R_{BC} (R_{CA} + R_{AB})}{(R_{AB} +R_{BC} + R_{CA})}[/Tex] → (2)

[Tex]R_C + R_A = \frac{R_{CA} ( R_{AB}+R_{BC})}{(R_{AB} +R_{BC} + R_{CA})}[/Tex] → (3)

Subtracting equation (2) from equation (1)

[Tex]R_A + R_B -(R_B + R_C)= \frac{R_{AB} (R_{BC} + R_{CA})}{(R_{AB} +R_{BC} + R_{CA})}-\frac{R_{BC} (R_{CA} + R_{AB})}{(R_{AB} +R_{BC} + R_{CA})}[/Tex]

[Tex]R_A-R_C=\frac{R_{BC} R_{CA}-R_{AB}R_{CA}}{R_{AB} +R_{BC} + R_{CA}} [/Tex]→ (4)

Add equation (3) and (4)

[Tex]R_C + R_A +R_A-R_C=\frac{R_{CA} ( R_{AB}+R_{BC})}{(R_{AB} +R_{BC} + R_{CA})}+ \frac{(R_{BC} R_{CA}-R_{B}R_{CA})}{(R_{AB} +R_{BC} + R_{CA})}[/Tex]

[Tex]2 R_{A} = \frac{(2R_{AB}R_{CA})}{(R_{AB} +R_{BC} + R_{CA})}[/Tex]

[Tex]R_A = \frac{(R_{AB}R_{CA})}{(R_{AB} +R_{BC} + R_{CA})}[/Tex] → (5)

Similarly,

[Tex]R_B =\frac {R_{AB}R_{BC}}{R_{AB} +R_{BC} + R_{CA}}[/Tex] →(6)

[Tex]R_C = \frac{R_{BC}R_{CA}}{R_{AB} +R_{BC} + R_{CA}}[/Tex] →(7)

Here R_A,R_B,R_C are the Resistors in star connection.

Star to Delta Conversion

To get the delta connection resistors R_AB,R_BC,R_CA from the star connection, Consider the star connection as shown below:

Star to Delta Conversion

Divide equation (5) by equation (6),

[Tex]\frac{R_A}{R_B}=\frac{\frac{R_{AB}R_{CA}}{R_{AB} +R_{BC} + R_{CA}}}{\frac{R_{AB}R_{BC}}{R_{AB} +R_{BC} + R_{CA}}}[/Tex]

[Tex]\frac{R_{A}}{R_{B}}=\frac{R_{CA}}{R_{BC}}[/Tex]

RCA=(RARBC)/RB[Tex]R_{CA}=\frac{R_{A}R_{BC}}{R_B}[/Tex]

Similarly divide equation (5) by equation (7),

[Tex]\frac{ R_A}{R_C}=\frac{R_{AB}}{R_{BC}}[/Tex]

[Tex]R_{AB} =\frac{R_AR_{BC}}{R_C}[/Tex]

Substitute R_AB, R_CA in equation (5),

[Tex]R_A=\frac{\frac{(R_AR_{BC})^{2}}{R_BR_C}}{\frac{R_AR_{BC}}{R_C}+\frac{R_AR_{BC}}{R_B}+R_{BC}}[/Tex]

[Tex]R_A=\frac{(R_AR_BC)^{2}}{R_AR_BR_{BC}+R_AR_CR_{BC}+R_BR_CR_{BC}}[/Tex]

[Tex]1 = \frac{(R_AR_{BC})^{2}}{R_{BC}(R_AR_B+R_AR_C+R_BR_C)}[/Tex]

[Tex]1 =\frac{R_AR_{BC}}{R_AR_B+R_AR_C+R_BR_C}[/Tex]

[Tex]R_AR_B+R_AR_C+R_BR_C=R_AR_{BC}[/Tex]

[Tex]R_{BC}=R_B+R_C+\frac{R_BR_C}{R_A}[/Tex]

Similarly,

[Tex]R_{AB}=R_{A}+R_{B}+\frac{R_AR_B}{R_C}[/Tex]

[Tex]R_{CA}=R_C+R_A+\frac{R_CR_A}{R_B}[/Tex]

Solved Example Based on Conversion

Find the equivalent delta connection of the circuit in star with resistances 2, 4 and 6 ohms respectively.

Consider the circuit,

RA= 2Ω, RB=4Ω, RC=6Ω

Star to Delta Connection

Substitute these values into the conversion formulas,

[Tex]R_{AB}=R_A+R_B+\frac{R_AR_B}{R_C}[/Tex]

[Tex]R_{AB}= 2 + 4+\frac{2\times4}{6}[/Tex]

[Tex]R_{AB}= 6+\frac{4}{3}[/Tex]

[Tex]R_{AB}=\frac{22}{3} Ω[/Tex]

Similarly,

[Tex]R_{BC}=R_B+R_C+\frac{R_BR_C}{R_A} [/Tex]

[Tex]R_{BC}= 4 + 6+\frac{4\times6}{2} [/Tex]

[Tex]R_{BC}=22 Ω[/Tex]

Similarly,

[Tex]R_{CA}=R_C+R_A+\frac{R_CR_A}{R_B} [/Tex]

[Tex]R_{CA}= 6 + 2+\frac{6\times2}{4} [/Tex]

[Tex]R_{CA}= 11 Ω[/Tex]

For the resistances RA= 2Ω, RB=4Ω, RC=6Ω in star connection the Equivalent resistances in delta connection are RAB=22/3 Ω,RBC=22 Ω,RCA= 11 Ω

Comparison Between Star and Delta Connection

Star Connection	Delta Connection
Also called as ‘ Y’ or ‘Wye’ connection	Also called as Mesh Connection.
It is a 4- wire connection	It is a 3- wire connection
The common point in star connection is called Neutral or star point.	There is no neutral point in delta connection.
Line Voltage is root three times phase voltage i.e. VL=√3 VP	Line Voltage is equal to the phase voltage i.e. VL=VP
Line current is equal to the phase current i.e. IL=IP	Line current is root three times phase current i.e. IL=√3 IP
Star connection is used for long distances	Delta connection is used for short distances.

Conclusion

In conclusion, this article discusses the star and delta connections used in the transmission and distribution of power. We discussed about star and delta connection starting with their definition, advantages, disadvantages, applications. In this article we can see that the star-connection is used for long distances due to the insulation required is less and achieve load balance because of neutral wire or conductor compared to the delta connection which doesn’t have any neutral wire unless if we provide it artificially. Based on the preferences and usability star connection can be converted into delta connection and vice versa, so that the advantages like Higher reliability, lesser cost delta connection is used and for the application of both transmission and distribution networks star connection is used.

FAQs on Star and Delta Connection

What is the Total power for star Connection ?

Consider,

The total power = 3 E_P I_P cosΦ

we know that E_P = V_L/√3, I_P =I_L

Then,

Total power (P)= 3 ( V_L/√3) I_L cosΦ

Total power (P) = √3V_L I_L cosΦ

What is the Expression for star-delta conversion?

From start to delta conversion, delta connected resistance is equal to the sum of the two resistance it is connected and the product of the two resistances divided by the remaining resistance.

For Example, In star connection the resistors are represented as R_a ,R_b , R_c then in delta connection the resistances are,

R₁=R_a+R_b+(R_a*R_b)/R_c, R₂=R_b+R_c+(R_b*R_c)/R_a, R₃=R_a+R_c+(R_a*R_c)/R_b.

What is the required voltage for star and delta connections ?

The required voltage for star connection is each winding receives 220V or 230V and the required voltage for delta connection is each winding receives 414V or 415V.