Star to Delta Conversion

In this article we will discuss about star to delta conversion. We will first discuss about star and delta connections, current and voltage equations in these circuits. Then we will discuss about the differences between the star and delta connection. We will also discuss in detail the steps followed to derive the equations for conversion. In addition to this we will look into some solved examples that will help us understand the concept better. Later in the article we will discuss about the applications, advantages and disadvantages of this conversion.

What is Star and Delta Connection?

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 Circuit

Star connection circuit is the circuit where the three resistor in the circuit have a common point. The shape of the circuit can be in the shape of ‘Y’ and ‘T’ alphabet or we say star shape. The common point is grounded in most cases. 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

Delta Connection Circuit

Delta connection is the type of connection where the three resistors are connected in a such way that they form a loop and they every two resistors have a common node. 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. This connection type is used in high voltage transmission system.

Delta Connection

Characteristics of Star and Delta Connection

Some of the important characteristics of star and delta connection are as follows:

Current and Voltage in Star Connection

Let there be three phase voltages [Tex]V_R,V_Y,V_B [/Tex] and the line voltages are represented by [Tex]V_{RY},V_{YB},V_{BR} [/Tex]

[Tex]V_R=V_Y=V_B=V_{ph} \newline V_{RY}=V_R+(-V_Y)=V_R-V_Y \newline using \: vector \: parallelogram \: law \newline V_{RY}=\sqrt{V_R^2+V_Y^2+2V_RV_Y\cos60} \newline V_{RY}=\sqrt{V_{ph}^2+V_{ph}^2+2V_{ph}^2\cos60} \newline \therefore V_L=\sqrt3{V{ph}} [/Tex]

Star Connection

So we can say that line voltage = [Tex]\sqrt3 [/Tex] X phase voltage in a star connection.

Similarly for current from the figure we can see that the load is balanced.

[Tex]\therefore I_R=I_Y=I_B=I_{ph} [/Tex]

We know that line current is equal to phase current from the above equation. [Tex]I_L=I_{ph} [/Tex]

Current and Voltage in Delta Connection

Circuit and Phasor Diagram

From the phasor diagram

[Tex]I_R=I_{BR}-I_{RY} \newline I_Y=I_{RY}-I_{YB} \newline I_B=I_{YB}-I_{BR} \newline using \: vector \: parallelogram \: law \newline I_R=\sqrt{I_{BR}^2+I_{RY}^2+2I_{BR}I_{RY}\cos60} [/Tex]

for Balanced load. [Tex]I_{RY}=I_{BR}=I_{YB}=I_{ph} [/Tex]

[Tex]\therefore I_R=\sqrt{I_{ph}^2+I_{ph}^2+2I_{ph}^2\cos60} \newline I_L=\sqrt3I_{ph} [/Tex]

As,[Tex]V_{RY}=V_{YB}=V_{BR}=V_L \newline \therefore V_L=V_{ph} [/Tex]

Difference Between Star and Delta Connection

Star Circuit	Delta Circuit
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.
One terminal is common for all the branches in the circuit.	for every two branch one terminal remains common.
[Tex]I_l=I_{ph} [/Tex]	[Tex]I_l=\sqrt3I_{ph} [/Tex]
[Tex]V_l=\sqrt3 V_{ph} [/Tex]	[Tex]V_l=V_{ph} [/Tex]
There is a neutral point present in the circuit	No neutral point is present in this type of circuit
It receives less power than the supply.	It receives the full power
Used in power transmission networks	Used in power distribution networks
It can have both balanced and unbalanced load	It can only have balanced load.

Star to Delta Conversion

The resistances of star connection from delta connection are,

[Tex]R_A=\frac{R_1R_2}{R_1+R_2+R_3} \newline R_B=\frac{R_2R_3}{R_1+R_2+R_3} \newline R_C=\frac{R_3R_1}{R_1+R_2+R_3} [/Tex]

Star Connection

Now, to express the resistance of delta network in terms of star network we use the above equations. first we multiply set of two resistances and then add the three sets. After simplifying we will get the following equation.

[Tex]R_AR_B+R_BR_C+R_AR_C= \frac{R_1R_2R_3}{R_1+R_2+R_3} [/Tex] -(1)

Delta connection

The above equation(1) is now divided by the equation of R_B ,

[Tex]\frac{R_AR_B+R_BR_C+R_AR_C}{R_B}=R_1 \newline \Longrightarrow R_1 =R_C+R_A+\frac{R_CR_A}{R_B} [/Tex]

The equation(1) is now divided by the equation of R_C ,

[Tex]R_2 =R_A+R_B+\frac{R_AR_B}{R_C} [/Tex]

The equation(1) is now divide by the equation of R_A ,

[Tex]R_3 =R_B+R_C+\frac{R_BR_C}{R_A} [/Tex]

The above three equation can be used to convert the star connection into delta connection.

Step By Step Approach of Star to Delta Conversion

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

Solved Example on Star to Delta Conversion

1. Given a network of 9 resistors, find the equivalent resistance between point E and F.
The connection between A, B, C is in delta connection which is converted to its equivalent star connection with the common node O

[Tex]R_{AO}=\frac{4X6}{2+4+6}=2 \Omega \newline R_{BO}=\frac{2 X 6}{2+4+6}=1\Omega \newline R_{CO}=\frac{2 X 4}{2+4+6}=\frac{2}{3}\Omega [/Tex]

Star to Delta Conversion

The network can be further simplified by adding the resistances in series combination i.e. [Tex]R_{DO}=2+6=8 \Omega \newline R_{EO}= \frac{2}{3}+\frac{10}{3}=\frac{12}{3}=4\Omega \newline R_{FO}=7+1=8\Omega [/Tex]

Star to Delta Conversion

Now again the star connection in the inner part of the triangle is again converted into delta connection.

[Tex]R_1=4+8+\frac{8X4}{8}=16\Omega \newline R_2=8+8+\frac{8X8}{4}=32\Omega \newline R_3=8+4+\frac{8X4}{8}=16\Omega [/Tex]

Star to Delta Conversion

Now, we will apply parallel combination between the nodes DG and EI, EI and FH, FH and DG.

After that we will get the resistances as, [Tex]R_{DE}=8\Omega \newline R_{EF}=8\Omega \newline R_{FD}=\frac{32}{3}\Omega [/Tex]

Star to Delta conversion

The equivalent resistance between E and F will be

[Tex]R_{EF}=\frac{8 X(8+32/3)}{8+(8+32/3)}=\frac{8X56}{80}=5.6 \Omega [/Tex]

2. Find the current drawn from the 5v battery in the network given below.

Star to Delta Conversion

Let us consider some points in the given network as A, B, C, D and G. If we consider the points A, B, C, D we can see that it is in star connection with common point as B.

Star to Delta Conversion

Converting it into delta connection,

[Tex]R_1=2+2+\frac{2X2}{3}=\frac{16}{3} \Omega \newline R_2=2+3+\frac{2X3}{2}=8 \Omega \newline R_3=2+3+\frac{2X3}{2}=8 \Omega [/Tex]

Star to Delta Conversion

Now applying the parallel combination we get resistances as[Tex]R_{AD}=\frac{8}{9}\Omega \newline R_{AC}=\frac{16}{3}\Omega \newline R_{CD}=\frac{8}{3}\Omega [/Tex]

Star to Delta Conversion

Now we will use parallel combination and series combination to find an equivalent resistance,

[Tex]\frac{\frac{16}{3}X\frac{32}{9}}{\frac{16}{3}+\frac{32}{9}}=\frac{32}{15}\Omega \newline \frac{32}{15}+3=\frac{77}{15}\Omega [/Tex]

Star to Delta conversion

From the above circuit, we can calculate the value of I as [Tex]I=\frac{5}{77/15}=0.974A [/Tex]

Applications of Star to Delta Conversion

• Its common application is to analyze and simplify complex circuits. It thus helps in easier calculation and less time consuming methods.
• It is used in power distribution systems, where loads are connected in either star or delta connection. Depending on the parameters the connection type is fixed. The conversion method gives the flexibility in changing the connection type as per requirement and analysis.
• It is used in impedance matching of a load with source which helps in optimizing the efficiency of power transfer.
• It is used in three-phase motors where the conversion method gives the flexibility of changing the connection type depending on the scenarios.

Advantages and Disadvantages of Star to Delta Conversion

There are some list of Advantages and Disadvantages of Star to Delta Conversion given below :

Advantages of Star to Delta Conversion

• Its use gives a easy approach for simplification of complex circuits.
• It gives flexibility in choosing the right connection type as per the requirements.
• It is used in step-up and step-down of voltages and currents depending on the connection type.
• It is highly compatible with three phase system.

Disadvantages of Star to Delta Conversion

• It is not applicable everywhere and mostly limited to three phaser system.
• Sometimes conversion can lead to voltage imbalance.
• It is not suitable for all type of loads and work only for specific types of load.
• It increases the complexity of circuits when applied to simple circuits.

Conclusion

Star and Delta are two types of connections that are used to simplify and analyze complex electrical circuits. They are mainly implemented to the three phase networks and are widely used for power distribution and circuit design. The process of expressing the resistances of delta connection in terms of star provides three equations to convert a star network into a delta network. This technique is quite useful as it gives the flexibility of changing the connection type as the required parameters. Although it is very useful but there certain limitation as well which includes it being mostly limited to three phase networks.

FAQs on Star to Delta Conversion

Why conversion from star to delta is required?

The conversion is needed when we have to change the circuit design for simplification process. It is also done for optimizing the electrical circuit for various applications.

What is the main difference between star and delta?

The main difference between in star and delta is the presence of common node in star connection and its absence in the delta connection. This will also make the shape of both the circuits different.

When is star connection and delta connection preferred?

Star connection is preferred when there is a neutral point required or when the load is unbalanced. Delta connection is preferred in case of high voltage transmission and when common point is not required.