Star to Delta and Delta to Star Transformation – Y-Δ Conversion
In an electrical network, the impedance can be connected in various configurations. The most common of these configurations are either star or delta connected network. To solve complex electrical networks or simplify it, we use the star-delta conversion technique. It replaces any star connected network with its equivalent delta connected network & vice versa. We are going to provide a brief formula derivation for load conversion between star and delta connected load.
Star Delta Conversion
We know the basic of series, parallel or combo of series and parallel connection but Y-Δ is another little bit complex configuration of components. The 3-phase networks have three wires and usually, the networks are connected in star & delta configuration. The 3 phase supply or the load connected in either formation can be converted into its equivalent counterpart. We use such conversion to simplify the mathematical calculations required for circuit analysis of a complex electrical network.
Delta Connected Network
The delta connected network is formed when three network branches or impedances are connected to form a loop in such a way that their heads are connected to the tails of the adjacent branch. The resultant network forms a triangle shape that resembles a Greek letter Delta “Δ” which is why it’s named after it. It is also known as π (pi) network because it resembles the letter after rearranging the branches. Know more about Delta Connection in the previous post.
Star Connected Network
The Star connected network is formed when three branches or impedances are connected together at a common point. The other ends of the branch networks are free. The resultant shape resembles the letter “Y” which is why it is also called “Y” or “Wye” connected network. It is also known as “T” connected network due to its shape after rearranging the network branches. Know more about Star Connection in the previous post.The circuits given above can be converted using the following transformation. During the transformation, the terminals A, B, C must remain in the same position, only the impedance & their arrangement changes. The following figure illustrates the statement given above.
Delta to Star Conversion
The delta connected network can be transformed into star configuration using a set of electrical formula. Let’s derive the equation for each impedance.The given figure shows a delta network having A, B, C terminals with the impedances R1, R2, R3. The equivalent star connected network with RA, RB & RC where they are connected to their corresponding terminals as shown in the figure.
As mentioned earlier, the terminals A, B, C remains the same, as well as the impedance between them, must remain the same.
RAB = RA + RB
RBC = RB + RC
RAC = RA + RC
First, Subtract (ii) from (iv)Similarly subtracting (i) & (iii) from (iv) results inFrom the derived equations for star-equivalent impedances RA, RB, & RC we can conclude the relation between delta-to-star conversions as; the equivalent star impedance is equal to the product of the adjacent delta impedances with a terminal divide by the sum of all three delta impedances.
In case all three Impedances are same in a delta network, the equivalent star impedance would become
Star to Delta Conversion
Now we are going to convert the star connected impedance into delta connected impedance. Let’s derive the equations used for a star to delta conversion.
In order to find the equivalent delta resistance, multiply the previous equation (v) & (vi), as well as (vi) & (vii) & (v) & (vii) together.
The relation between star to delta equivalent impedance is clear from the given equation. The sum of the two-product of all star-impedances divide by the star impedance of the corresponding terminal is equal to the delta impedance connected with the opposite terminal.
Using the previous equation,
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