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To convert a delta network to an equivalent star network we need to derive a transformation formula for equating the various resistors to each other between the various terminals. Consider the circuit below.

Delta to Star Network.

Delta to Star Transformation

Compare the resistances between terminals 1 and 2.

Resistance Between Terminals 1 and 2

Resistance between the terminals 2 and 3.

Resistance Between Terminals 2 and 3

Resistance between the terminals 1 and 3.

Resistance Between Terminals 1 and 3

This now gives us three equations and taking equation 3 from equation 2 gives:

Resistance equation

Then, re-writing Equation 1 will give us:

Resistance equation

Adding together equation 1 and the result above of equation 3 minus equation 2 gives:

Resistance equation

From which gives us the final equation for resistor P as:

Resistance P

Then to summarize a little the above maths, we can now say that resistor P in a Star network can be found as Equation 1 plus (Equation 3 minus Equation 2) or   Eq1 + (Eq3 – Eq2).

Similarly, to find resistor Q in a star network, is equation 2 plus the result of equation 1 minus equation 3 or  Eq2 + (Eq1 – Eq3) and this gives us the transformation of Q as:

Equivalent Resistance Q

and again, to find resistor R in a Star network, is equation 3 plus the result of equation 2 minus equation 1 or  Eq3 + (Eq2 – Eq1) and this gives us the transformation of R as:

Equivalent Resistance R

When converting a delta network into a star network the denominators of all of the transformation formulas are the same: A + B + C, and which is the sum of ALL the delta resistances. Then to convert any delta connected network to an equivalent star network we can summarized the above transformation equations as:

Delta to Star Transformations Equations

Equivalent Resistance PEquivalent Resistance QEquivalent Resistance R

Example No1

Convert the following Delta Resistive Network into an equivalent Star Network.

Delta to Star ExampleDelta to Star Equations

Star Delta Transformation

We have seen above that when converting from a delta network to an equivalent star network that the resistor connected to one terminal is the product of the two delta resistances connected to the same terminal, for example resistor P is the product of resistors A and B connected to terminal 1. By rewriting the previous formulas a little we can also find the transformation formulas for converting a resistive star network to an equivalent delta network giving us a way of producing a star delta transformation as shown below.

Star to Delta Network.

Star to Delta Transformation

The value of the resistor on any one side of the delta, Δ network is the sum of all the two-product combinations of resistors in the star network divide by the star resistor located “directly opposite” the delta resistor being found. For example, resistor A is given as:

Resistor A

with respect to terminal 3 and resistor B is given as:

Resistor B

with respect to terminal 2 with resistor C given as:

Resistor C

with respect to terminal 1.

By dividing out each equation by the value of the denominator we end up with three separate transformation formulas that can be used to convert any Delta resistive network into an equivalent star network as given below.

Star Delta Transformation Equations

Equivalent Resistance AEquivalent Resistance BEquivalent Resistance C

One final point about converting a star resistive network to an equivalent delta network. If all the resistors in the star network are equal in value then the resultant resistors in the equivalent delta network will be three times the value of the star resistors and equal, giving:   RDELTA = 3RSTAR

Reference: Electronics Tutorials

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  1. nazeer ahamed
    Jan 29, 2020

    is that possible Dyn11 to YNyno to YNd11 to parallel in Transformers, any special considerations to take to connect in parallel.

  2. Atul Anchal
    Mar 16, 2015

    i want to work on a innovative project.and i hope from this portal that it help me

  3. Wayne Storr
    Feb 21, 2014

    Nice plagiarized article from my site, including images, well done. May I plagiarized your site as well. i need some new content.

    • Edvard
      Feb 21, 2014

      Hi Wayne, I’m truly sorry for this and other theorems being practically stolen without your permission as owner. They were published in the very early stage of EEP few years back. I could add your website as the reference or even remove these pages from EEP. Which option suits you best?

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thirty two  ⁄    =  eight

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