Y-Δ Conversion: Transformation | Diagram & Formula

Y-Δ Conversion: Transformation | Diagram & Formula

One of the most commonly used conversion methods in three-phase electric circuit analysis is the transformation of star delta. In addition, there are some complex circuits that make it difficult to determine whether a series circuit or a parallel circuit can be easily solved by converting Star Delta.

Today we will discuss in detail the process of converting from Star Connection to Delta Connection and Delta Connection to Star Connection.

What is going on in our discussion today:

  • Introduction.
  • What is Star Connection?
  • What is Delta Connection?
  • Transition from Star Connection to Delta Connection.
  • Transition from Star Delta to Delta Connection.

Introduction

1899 In Arthur Edwin Kennelly The theory of circuit transformation was first published. 

star delta transformation
Arthur E. Kennelly ( 1861 – 1939)

The Star-Delta transformation is known by various names such as the Wi-Delta (Y-Δ) Conversion, Star-Mash Transformation, T-Pie (T-Π) Conversion. This conversion method is more commonly known as Star Delta or Wi Delta transformation. These are named based on the size of the circuit diagram. Note that in the Finnish language, Y is called a star. We will use the words Star and Delta in our discussions. 

What is Star Connection?

The connection to which the conductors’ resistances are connected at a certain point is called a star connection.

A star connection is shown below:

star delta transformation
Star Connection

What is Delta Connection?

The connection in which the conductors’ resistances are connected in a triangular shape is called a delta connection.

A delta connection is shown below:

star delta transformation
Delta Connection

Conversion from Star Connection to Delta Connection:

By multiplying the two resistances periodically from the star connection, the sum of these resistances will be added by dividing the sum of the resistances on the opposite side of the resistor which we will calculate.

Examples:

star delta transformation
Star Connection

Ra, Rb And Rc There is a star connection with resistance. This connection has to be converted to a delta.

To convert, we first imagined a delta connection above the star connection.

star delta transformation
Delta connection drawn on star connection

Now if we follow the above procedure,R1, R2 And R3    Determine, then we will first connect the two resistances together by connecting them to the star connection.

That is,  RaRb + RbRc + RcRa

Since we R1 Since to diagnose R1 On the contrary, the resistance of the star connection Rc By RaRb + RbRc + RcRa Will share

Therefore R1 The equation is, 

star delta transformation

The equation is, R2 And R The equation is,

star delta transformation

In the above method of solving mathematical problems Ra, Rb, And Rc  In the above method of solving mathematical problems… 

Transition method from Delta to Star connection

The sum of the two delta resistances connected at a certain end of the delta connection must be divided by the sum of the three resistances at the connection.

Examples: 

star delta transformation
Delta Connection

R1, R2 And R3There is a delta connection with resistance. This connection needs to be converted to a star.

To convert, we first plotted a star connection inside the delta connection.

star delta transformation
Star connection numbered inside delta connection

Now, according to the above method Ra, Rb And Rc I will determine.

If Ra If you want to determine the two delta resistance associated with it  R1 And R2  Its resistance is multiplication 3 T R1, R2 And R3 Must be divided by the sum of 

That is,

star delta transformation

How

star delta transformation

In the above method of solving mathematical problems R1, R2 And R3  Instead, we can easily convert the delta connection to a star connection by setting the value specified in the query.

References:

Fundamentals of Electric Circuits by Alexander & Sadiku

Wikipedia

Electrical4u

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