Star And Delta Conversion
Slikk Huisenga
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.
Standard 3-phase circuits or networks take on two major forms with names that represent the way in which the resistances are connected, a Star connected network which has the symbol of the letter, Υ (wye) and a Delta connected network which has the symbol of a triangle, Δ (delta).
If a 3-phase, 3-wire supply or even a 3-phase load is connected in one type of configuration, it can be easily transformed or changed it into an equivalent configuration of the other type by using either the Star Delta Transformation or Delta Star Transformation process.
Having now defined exactly what is a Star and Delta connected network it is possible to transform the Υ into an equivalent Δ circuit and also to convert a Δ into an equivalent Υ circuit using a the transformation process.
This process allows us to produce a mathematical relationship between the various resistors giving us a Star Delta Transformation as well as a Delta Star Transformation.
These circuit transformations allow us to change the three connected resistances (or impedances) by their equivalents measured between the terminals 1-2, 1-3 or 2-3 for either a star or delta connected circuit.
However, the resulting networks are only equivalent for voltages and currents external to the star or delta networks, as internally the voltages and currents are different but each network will consume the same amount of power and have the same power factor to each other.
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.
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:
If the three resistors in the delta network are all equal in value then the resultant resistors in the equivalent star network will be equal to one third the value of the delta resistors. This gives each resistive branch in the star network a value of: RSTAR = 1/3*RDELTA which is the same as saying: (RDELTA)/3
The transformation from a Star network to a Delta network is simply the reverse of above. We have seen 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 connected network to an equivalent delta network giving us a way of producing the required transformation as shown below.
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.
One final point about converting a star connected resistive network into an equivalent delta connected network. If all the resistors in the star network are all 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 = 3*RSTAR
Both Star Delta Transformation and Delta Star Transformation allows us to convert one type of circuit connection into another type in order for us to easily analyse the circuit. These transformation techniques can be used to good effect for either star or delta circuits containing resistances or impedances.
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.
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.
A Delta Star conversion is a method of transforming a circuit from a delta (Δ) configuration to a star (Y) configuration. It involves rearranging the resistors or other components in a way that changes the circuit's topology.
Delta Star conversion is useful for simplifying complex circuits and analyzing their behavior. It can help reduce the number of components and make calculations easier by converting the circuit into a more manageable form.
To perform a Delta Star conversion, you need to identify the delta and star configurations in the circuit. Then, you can use the appropriate conversion equations to determine the new values of the components. Finally, rearrange the components according to the new configuration.
One advantage of Delta Star conversion is that it simplifies circuit analysis by reducing the number of components. It also helps in designing circuits with specific impedance or voltage requirements. Additionally, it can help identify faulty or malfunctioning components in a circuit.
Yes, there are a few limitations to Delta Star conversion. It may not be applicable to all types of circuits, and the conversion may introduce errors in the circuit's behavior. Also, the conversion equations may not work for circuits with non-linear components, such as diodes or transistors.
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
In this book, the three-phase ac systems are considered as a balanced circuit, made up of a balanced three-phase source, a balanced line, and a balanced three-phase load. Therefore, a balanced system can be studied using only one-third of the system, which can be analyzed on a line to neutral basis.
The star-delta (Y-Δ) or delta-star (Δ-Y) conversion (Fig. 3-15) is required in three-phase ac systems to simplify the circuits and ease their analysis. If a three-phase supply or a three-phase load is connected in delta, it can be transformed into an equivalent star-connected supply or load. After the analysis, the results are converted back into their original delta equivalent.
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