Star To Delta Transformation
Leontina Heidgerken
In electrical engineering, the Y-Δ transform, also written wye-delta and also known by many other names, is a mathematical technique to simplify the analysis of an electrical network. The name derives from the shapes of the circuit diagrams, which look respectively like the letter Y and the Greek capital letter Δ. This circuit transformation theory was published by Arthur Edwin Kennelly in 1899.[1] It is widely used in analysis of three-phase electric power circuits.
The transformation is used to establish equivalence for networks with three terminals. Where three elements terminate at a common node and none are sources, the node is eliminated by transforming the impedances. For equivalence, the impedance between any pair of terminals must be the same for both networks. The equations given here are valid for complex as well as real impedances. Complex impedance is a quantity measured in ohms which represents resistance as positive real numbers in the usual manner, and also represents reactance as positive and negative imaginary values.
Resistive networks between two terminals can theoretically be simplified to a single equivalent resistor (more generally, the same is true of impedance). Series and parallel transforms are basic tools for doing so, but for complex networks such as the bridge illustrated here, they do not suffice.
Every two-terminal network represented by a planar graph can be reduced to a single equivalent resistor by a sequence of series, parallel, Y-Δ, and Δ-Y transformations.[3] However, there are non-planar networks that cannot be simplified using these transformations, such as a regular square grid wrapped around a torus, or any member of the Petersen family.
In graph theory, the Y-Δ transform means replacing a Y subgraph of a graph with the equivalent Δ subgraph. The transform preserves the number of edges in a graph, but not the number of vertices or the number of cycles. Two graphs are said to be Y-Δ equivalent if one can be obtained from the other by a series of Y-Δ transforms in either direction. For example, the Petersen family is a Y-Δ equivalence class.
During the analysis of balanced three-phase power systems, usually an equivalent per-phase (or single-phase) circuit is analyzed instead due to its simplicity. For that, equivalent wye connections are used for generators, transformers, loads and motors. The stator windings of a practical delta-connected three-phase generator, shown in the following figure, can be converted to an equivalent wye-connected generator, using the six following formulas[a]:
The resulting network is the following. The neutral node of the equivalent network is fictitious, and so are the line-to-neutral phasor voltages. During the transformation, the line phasor currents and the line (or line-to-line or phase-to-phase) phasor voltages are not altered.
If the actual delta generator is balanced, meaning that the internal phasor voltages have the same magnitude and are phase-shifted by 120 between each other and the three complex impedances are the same, then the previous formulas reduce to the four following:
For those who can't see the image:SO there is an outer delta with two 1 ohms and a 2 ohm. Then an inner Y with three 2 ohms. Within the Y, there is a delta formed on it's two lower legs with three 1 ohms. The question is to find the resistance between the upper arm above the inner delta.
Here's my take on the problem.I'll do it graphically, just to show the transformations I'd do, no math.I'll use IEC+ANSI instead of NEMA symbols, because I'm more used to them, and it's easier to draw a rectangle in MS Paint than a sawtooth line.
We end up with image [5(first)] and with a bit of different layout [5(second)] we see that R4 and R6 are in parallel. Then in series with R5. Then in parallel with Red resistor. Then we'got just one resistor left = the answer.
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.
This article focuses on Star and Delta connection. We will discuss its circuits, transformations, differences and Solved examples. The information in this article helps you extensively in your SSC JE Electrical and GATE Electrical preparation journey.
Star and delta connections are two types of electrical connections used in three-phase power systems. In a star connection, three phases are connected at a central point, while in a delta connection, the three phases are connected in a loop. The choice between these connections depends on the power requirements and the type of load being supplied.
In a 3-phase circuit, there are two types of connections: Star and Delta. A Star Connection is a 4-wire system where the line voltage is root three times the phase voltage. It is primarily a balanced circuit connection as the neutral wire carries unbalanced current to the ground. On the other hand, a Delta Connection is a 3-wire system where the line voltage is equal to the phase voltage. Delta connections are mostly unbalanced circuits since they lack a neutral wire.
Star and Delta connections are two types of connections used in 3-phase circuits. In a Star Connection, the system has a neutral wire, and the line voltage is root three times the phase voltage. It is a balanced circuit connection. In a Delta Connection, there is no neutral wire, and the line voltage is equal to the phase voltage. It is commonly an unbalanced circuit connection.
A star circuit is one in which similar ends of three resistances are connected to a common point 'N' called a star point or neutral point. It is also called Wye or Tee (T) connection because of its shape, as shown in the figure below.
In both systems, the voltage between two phases is referred to as the "line voltage," while the voltage between phases and the neutral is referred to as the "phase voltage" (line to neutral). Single-phase voltage is the voltage between any line (or phase) and neutral, whereas three-phase voltage is the voltage between all three lines (or phases). Remember that the power in both systems is always the same and equal since different levels of voltages and currents are only ever employed in various systems depending on the situation.
Thus the equivalent delta resistance between two nodes is the sum of two-star resistances connected to those nodes plus the product of the same two-star resistances divided by the third star resistance.
When we study the circuit of star connection, we can see that the line is in series with its respective phase winding. Therefore, we can conclude that in star connection the line current is equal to the phase current.
This article subsumes all the information related to star delta connection, you need to propel your preparation for various AE/JE examinations. To reinforce your preparation, you should test yourself through a myriad of Mock Tests for Electrical Engineering Exams. You can check the syllabus for the AE/JE exam. You can visit the Testbook app to keep yourself updated with all the exam-oriented information related to the upcoming examinations, including Electrical Gate Exam, SSC JE, and RRB JE
The Y-Δ (wye-delta) and Δ-Y (delta-wye) transformations are used to calculate the resistances in the corresponding Δ or Y circuit. These circuits consist of three resistors connected as in the image below.
Resistors are the most fundamental components in building of any electrical circuit, because of this most circuits constitutes of multiple resistors and they have to be simplified to obtain the net resistance for the circuit analysis. The resistances are grouped in either star/wye or delta topology and for the complete network resolution they have to be inter-converted into one another as there is no other transformation.
In the previous chapter, we discussed about the conversion of delta network into an equivalent star network. Now, let us discuss about the conversion of star network into an equivalent delta network. This conversion is called as Star to Delta Conversion.
This document discusses star-delta (wye-delta) transformations of electrical circuits. It begins by introducing star and delta networks, then defines star-delta transformation as a method to simplify complex 3-phase resistive circuits. Six equations are presented to convert between star and delta configurations by relating resistances between nodes. An example calculation is shown to find the delta resistances RA, RB, and RC given the star resistances R1=80Ω, R2=120Ω, and R3=40Ω.Read less
I am here with a very confusing question. I have a theoretical submission on Star Delta Transformation and I have read many topics online and have cleared my concepts but the thing is I couldn't find any practical applications of it.
I mean we use it for converting Star design to Delta but someone could refer me any of its practical application i.e. why we use it? & How to use it in complex circuits. I have just seen calculations like formulas Derivation etc. here's one example, which I like the most, What is Star Delta Transformation? but haven't seen any practical circuit solving. like multiple branches of resistances in star format and then solve it by transforming it to delta or vice versa.
Star Delta Transformation is a method used to simplify and analyze complex electrical networks. It involves converting a circuit with a star (or Y) configuration to an equivalent delta (or Δ) configuration, or vice versa.
Star Delta Transformation is used to make calculations and analysis of electrical circuits easier and more efficient. It allows for the conversion of a circuit with mixed resistive and reactive elements to an equivalent circuit with only resistive elements, making it easier to apply Ohm's Law and other circuit laws.
Star Delta Transformation is applicable to circuits with three branches and a common point, where one branch is connected between each pair of elements. This type of circuit is commonly found in three-phase electrical systems.
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