Table of Content

• Star and Delta Connection
• Properties
• Star Vs Delta Connection
• Delta to Star Conversion
• Steps to Solve Conversion
• Solved Example
• Applications
• Advantages
• Disadvantages

Parameter	Star Connection	Delta Connection
Presence of Node	In this type of circuit the all the three branches have a common node and branches initiate form this node.	In this type of circuit the three are connected in way that they form a loop and no common node is present.
Common Terminal	One terminal is common for all the branches in the circuit.	For every two branches one terminal remains common.
Relation between line and phase current	IL=Iph	IL=√3 Iph
Relation between line and phase voltage	VL=√3 Vph	VL=Vph
Presence of neutral point	There is a neutral point present in the circuit	No neutral point is present in this type of circuit
Power Supply	It receives less power than the supply.	It receives the full power.
Used in	Used in power transmission networks	Used in power distribution networks
Load Type	It can have both balanced and unbalanced load	It can only have balanced load.

Delta to Star Conversion

Delta to Star Conversion allows to convert Delta circuit connection into Star circuit connection by formation of resistances in both the side. 

Let us consider three resistances R_AB, R_BC, R_AC are connected in delta to three terminals A, B and C

If this circuit is converted to star connection by three resistances R_A, R_B, R_C as shown here.

We are calculating equivalent circuit therefore, the resistance measured between any two of the terminals A, B, and C must be the same in two cases.

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

Mathematically, we can write

R_A+R_B=(R_BC+R_AC)R_AB/(R_AB+R_BC+R_AC) →1

R_B+R_C=(R_AB+R_AC)R_BC/(R_AB+R_BC+R_AC) →2

R_C+R_A=(R_AB+R_BC)R_AC/(R_AB+R_BC+R_AC) →3

Adding the above three equations

2(R_A+R_B+R_C)=2(R_ABR_BC+R_ACR_BC+R_ABR_AC)/(R_AB+R_BC+R_AC)

∴ R_A+R_B+R_C= (R_ABR_BC+R_ACR_BC+R_ABR_AC)/(R_AB+R_BC+R_AC) →4

Subtract Equation 2 from Equation 4

R_A+R_B+R_C−(R_B+R_C)=

equals (R_ABR_BC+R_ACR_BC+R_ABR_AC)/(R_AB+R_BC+R_AC) -(R_AB+R_AC)R_BC/(R_AB+R_BC+R_AC)

∴ R_A=R_ACR_AB/( R_AB+R_BC+R_AC)

Similarly, Subtract Equation 3 from Equation 4

R_B=R_BCR_AB/( R_AB+R_BC+R_AC)

Similarly, Subtract Equation 1 from Equation 4

R_c=R_ACR_BC/(R_AB+R_BC+R_AC)

We can use these relations to calculate the resistances of star network from the resistances of delta network

Steps to Solve Delta to Star Conversion

Let us summarize the steps to be followed for delta to star conversion :

• First the delta connection needs to be identified
• After identifying the circuit, label all the resistors and also label the nodes. Find the central node between two branches and accordingly label other nodes.
• Using the above derived equations find the equivalent star resistances.
• Now replace the delta connection with the star resistances and shape.
• Verify the connection and check the resistance values and their positions between the nodes.

Solved Example on Delta to Star Conversion

Find the equivalent star connection of the circuit in star with resistances R_ac=4 ohms ,R_bc=8 ,R_ab=12 ohms respectively.

From our previous derivations, we can say that

R_c=R_acR_bc/ (R_ac+R_ab+R_bc)

R_a=R_abR_ac/ (R_ac+R_ab+R_bc)

R_b=R_bcR_ab/ (R_ac+R_ab+R_bc)

we have R_ac=4 ,R_bc=8 and R_ab=12

On putting these values in above equation

R_c= 4*8/24 = 4/3 ohms

R_a= 4*12/24= 2 ohms

R_b= 8*12/24 = 4 ohms

The resistor value in a Y network that is equivalent to a Δ containing 3 resistors of R ohm.

A Y network means a star network. We are given that the three resistances in star connection are R ohms and we have to find the equivalent resistance in star connection. Consider the diagram

Given R_A=R_B=R_C=R ohms

R₁=R_AR_B/R_A+R_B+R_C

R₂=R_AR_C/R_A+R_B+R_C

R₃=R_CR_B/R_A+R_B+R_C

From symmetry of the question we can say

R₁=R₂=R₃

On putting the value R ohm ,we get

∴ R₁=R₂=R₃=R/3 ohms

Applications of Delta to Star Conversion

Let us see some applications of delta to star conversion

• The most common application is simplification of complex circuits which makes circuit analysis easier. It helps in making the calculations easier and less time-consumes even for circuits with complex parameters.
• It is used in connections involving transformers. Whenever there is a requirement of impedance matching in transformer, the windings of transformer can be arranged in star or delta configuration to match the impedance or the voltage.
• It is used in motors where it helps in optimizing the efficiency of connections. This can be done by arranging winding in different configurations to form a great power system.
• Delta and Star connections are used in high school education to simplify the understanding for students and help them understand complex circuits.
• The transformation circuits can be used for calculating power factor and even helps in correcting it using fault analysis. This helps in optimizing the performance by mitigating the errors.

Advantages of Delta to Star Conversion

Let us see some advantages of delta to star conversion

• It simplifies the task of solving of complex circuits. It is crucial for calculating currents, voltages, and power in the complex systems.
• It helps us in circuit designing as per our need due to various features provided by these circuits. Delta and star connection can serve the diverse needs and can meet specific requirements .
• Due to the ease of designing, they are a common choice for circuit design in everyday appliances like they are used in step-up and step-down motors.
• The transformation from one circuit to another circuit type allows us to identify any potential cause of error therefore helping in fault analysis.
• It allows impedance matching between the components of the system. This is particularly useful in transformers and motors.

Disadvantages of Delta to Star Conversion

Let us see some disadvantages of delta to star conversion

• There are some restrictions associated with using these connections. They are mostly used in three phaser system and there scope can’t expand beyond that.
• The manual application of these circuits can be a tedious task. This can be a major problem in circuits that require huge mathematical calculations.
• Sometimes, the transformation of circuits from one form to another can lead to inaccuracy between the original and transformed circuit. Therefore, it can introduce some errors in circuit.
• It increases the complexity of circuits when applied to simple circuits making it challenging to calculate the corresponding circuit values.
• Sometimes, implementing the transformed circuit can involve more components resulting in a complicated overall design of the circuit in addition to the increased overall cost of system.

Conclusion

We have studied two important types of circuit connections in this article. We have also seen the relationship between the different parameters of the Star and Delta circuits. In addition to this, we have seen how the two types of connection are different from each other and therefore, we devised the necessary equations that can be used to convert the delta circuit to a Star circuit. Although, this method is helpful but there are some limitations to it. Some solved examples have been provided for better understanding of the concept. Readers are requested to refer to FAQs in case any doubt still exists.

Delta to Star Conversion – FAQs

Which connection is better star or delta?

Bothe connections have their own benefits. Star connection is better for long-distance communication because it requires little insulation. Delta connections are used for small range of distances.

What is the main advantage of Delta connection?

The major advantage of delta connection is its high reliability. Even if one of the three primary windings fails ,the secondary coil continues to produce full voltage on all three phases. This is not seen in star connection.

What are some other connections apart from star and delta connections?

Some other useful connections apart from star and delta connections include Mesh connection, series connection, parallel connection, bridge connection, zig-zag connection.