Analyzing linear circuits, either AC or DC circuit, can be easy with simplification methods such as Theveninâ€™s or Nortonâ€™s theorem. Yet, these methods wonâ€™t work for all networks especially circuits that consist of 3 terminal networks. In this case, star delta transformation becomes useful.
The technique generally works like other theorems which can help simplify the networks. The circuits are commonly found in matching networks, phase networks, or electrical filters. Keep scroll through the points below to understand this useful technique.
Star Delta Transformation Explanation
According to the definition, star delta transformation or also known as wye-delta transformation is a technique that enables you to resolve different circuit in electrical systems. The technique can be applied to circuits with numerous resistance in a 3-phase configuration to another type of circuit connection.
The transformation technique was found in 1899 by Edwin Kennelly, an American electrical engineer. Aside from solving electrical system, the technique can also be used in planar graphs in math.
The basic 3-phase circuits come in two major forms represented by their names: Star and Delta networks. Star network is a connected network with the symbol of Y. Meanwhile, Delta network comes in a symbol of triangle or delta.
Whenever a 3-phase network is connected in a configuration, it can be transformed into an equivalent circuit. Either Delta star transformation or star delta transformation can be involved in the transformation process.
The star delta conversion is also known by a number of other names. Most of the names are based on the shapes of the configuration. The most popular names include Y (wye), T configuration, and Delta configuration because of its triangle shape.
Besides, there are also Pi because it resembles phi shape. Pi is also known as TT configuration. Another common name for the transformation is star-mesh.
The networks between 2 terminals can also be simplified into an equivalent resistor. The transformation can help eliminate one node to produce a simpler network. But for a complex circuits, the simplification is not possible. Though it is commonly used for a planar graph, it also works for non-planar networks.
Equivalent Network Transformation
A resistive network which consists of 3 impedances can be connected into a T configuration. However, the network can also be transformed into a Y or star network. On the other hand, other 3-phase networks such as Pi type can be reformed into other networks. Pay attention to the transformations below.
T-connected to star network
A T-network is a 3-phase configuration consisting of 2 resistors series and 1 resistor parallel. This network can be redrawn into an equivalent Start or Y network. Both configuration can produce equivalent electrical network.
Pi-connected to delta network
A Pi- or TT-resistor network is another configuration with 3 impedances. This type of network can be transformed into a delta network which is electrically equivalent.
Star to delta or vice-versa
Star or delta connected network can be transformed into one another with equivalent electric. It uses transformation process which produces a math relationship between resistors.
It is important to note that each resulting star delta transformation is equivalent for external voltages and currents. And yet, the internal voltages and currents are different though the network uses the same amount of power as well as has the same power factor.
How to Transform Star to Delta
Transforming star-type network to delta can be conducted in a few steps, which are actually the reverse of delta star transformation. To begin with, note that the resistor value of any side of delta network is the total of two combined resistors in star network divided by resistor across the found delta resistor.
Given that, equations can be made to find out the value of each resistor in delta network. Dividing every equation by denominator value, you can find three transformation formulas to convert delta resistive network into a star network.
Delta to Star Transformation
As the reverse of star delta transformation, delta star conversion transforms a delta-type network into an equivalent star-type network. To convert, you need to define a transformation formula. This is how you can equate resistors to each other among the existing terminals.
You can begin with drawing a delta network and its star equivalent network and name the terminals with 1, 2, and 3 and resistors with P, Q, and R. First, compare the resistance between terminals 1 and 2 with a specific equations. Then, calculate the resistance between terminals 2 and 3. Last, make another equation to compare resistance between terminals 1 and 3.
Now that you have three equations, subtract equation 3 by equation 2. Next, rewrite equation 1 and add with the result of equation 3 subtracted by equation 2 previously. From this equation, you can find the final equation for resistor P. Do the similar steps for other resistors, Q and R.
Benefits of Star Delta Transformation
Knowing the benefits of something allows you to get the best out of it. When it comes to star delta conversion, there are several advantages of using this transformation to your electrical circuits. The advantages include:
- Star transformation is applicable and suitable to long distance transport of voltages. The transformation also has a neutral point that can be employed to unbalanced transient current to the ground.
- Delta transformation is beneficial to transport 3-phase voltage in a balance condition. It does not have neutral wire which makes it the best choice for transmission network.
As with maximum power transfer and other methods, star delta transformation needs a proof. The proof of uniqueness and existence of this transformation can be given by considering three aspects: external voltage, nodes, and corresponding currents.
For external voltages at 3 nodes, the corresponding currents are exactly the same for star and delta circuits. Based on superposition theorem, instead of delivered by voltage sources, the voltages can be obtained by observing the superposition of voltages at the nodes. Kirchhoffâ€™s laws can be used to show the equivalence that the summed currents is equal to zero. Meanwhile, to get the same voltages at nodes, the equivalent resistance must be the same. You can use basic rules to resolve series or parallel networks to obtain the value.