Delta To Star Conversion Examples
Venice Sassone
In the previous chapter, we discussed an example problem related equivalent resistance. There, we calculated the equivalent resistance between the terminals A & B of the given electrical network easily. Because, in every step, we got the combination of resistors that are connected in either series form or parallel form.
However, in some situations, it is difficult to simplify the network by following the previous approach. For example, the resistors connected in either delta (δ) form or star form. In such situations, we have to convert the network of one form to the other in order to simplify it further by using series combination or parallel combination. In this chapter, let us discuss about the Delta to Star Conversion.
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.
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.
The above circuit is a delta configuration. To convert the delta circuit into an equivalent star network, use these formulas. To visualize while calculating the values of star-connected resistances, use this figure.
By observing the above equations of delta conversion, we can see that the equivalent delta resistance between any two-star terminals is given by the sum of both the star resistances plus the product of both these resistances divided by the third-star arm resistance.
Now that we know how to simplify the star or delta connected network, we can work on the first problem in figure 1(a). The R2, R4, and R6 resistors are in the delta-connected network. If we convert that to a star network, then the resultant network will look like this.
In the example, we did a Y-Δ transformation or a delta transformation to simplify the analysis of an electrical network. Similarly, we can do delta star transformation to simplify circuits. Once we get the star equivalent circuit, we can solve that with other series or parallel circuits.
The above image shows an example of the Δ-Y connection, which means Δ in primary winding and Y in a secondary winding of the transformer. Transformers have primary and secondary three-phase windings for stepping up or stepping down the voltage.
For transmission purposes, secondary winding should be in a delta connection; while for distribution purposes, secondary winding should be in star connection. We use the star connection for distribution because we get a neutral terminal at the center of the star connection.
In DC circuits, inductors act as closed-circuit while capacitors act as open circuits. Hence, these circuits can only be explained using resistance. In AC circuits, the combined resistive effect of resistors, capacitors, and inductors makes impedance. Although both resistance and impedance are denoted by R and Z, respectively, the unit we use for both impedance and resistance is Ω.
This topic is included in the curriculum of an undergraduate degree that includes the study of basic electrical and electronics such as electrical engineering, electronics and computer engineering, electronics and communication engineering, and so on.
Explanation: Using equations 1, 2, and 3, if one transforms DAC, which is a delta configuration to star configuration, they will get one resistor in series with one parallel circuit. Solving these, one will get 1.18 Ω resistance across the battery terminals.
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
Let's take a closer look at the different ways that are used in air compressors (and any industrial machine with electric motors). I will limit amount of theory about it and show you what this actually looks like in a real-life industrial air compressor.
DOL and Star-Delta starters use simple mechanical contactors (big relays) to start the motor. Softstarters and frequency drives use advanced mico-electronics to alter voltage and frequency during startup to greatly reduce the startup current. (think of a softstarter as a super simple frequency drive, only used during startup).
The electric diagram is also pretty simple. It consists of a single contactor (a big relay, or electrically controlled switch) that is closed by a signal from the main controller. The startup current of the motor is around 7 to 9 times the nominal running current.
3-phase asynchronous motor convert electric energy into rotational energy using a rotating magnetic field. The magnetic field is created with the help of different motor windings, or coils. These windings are fixed/stationary at the outside part of the motor (the stator).
Because of the 'rotating' 3-phase power supply (3 phases offset at 120 degrees), a rotating magnetic field is created. The rotor rotates inside the stator, at a slightly lower speed (rpm) - that's why they are called 'asynchronous' motors. The difference between the speed of the rotor and that of the magnetic field is called the 'slip' and is usually a few percent.
In the picture above you can see 6 wires/connections. Two are connected together by the interlink plates. In this example, the motor is hard-wired in a delta-configuration. The incoming 3-phase supply must be connected to each one of the pairs. If the motor was connected in a star-configuration, we would see the connecting plates all on one side, make a single star point.
In star - things are a bit more complicated: the phase-to-phase voltage (400 volt) is divided between two coils (and also passes through the center star connection) - the resulting voltage over each coil is 230 volt (400 volt / square root of 3).
The motor in this example is a 400/690 volt motor - if your electric system is 4400 volt, you should connect it in delta. If you have a 690 volt system - you should connect it in star. (note that the voltage over the winding is the same in both cases - in a star configuration, the voltage over the winding is 690 / sqr 3 = 400 volt).
Back to the startup systems... Star/delta (Y-D) is the most common system deployed in air compressors, or in industrial machines in general. It's simple, easy to understand, easy to troubleshoot and doesn't require expensive electronics.
Remember, the motor in our example has a nominal voltage of 400 in delta and 690 in star. If we have a 400 volt power supply and we connect this motor in star - we essentially connect a 690 volt motor to a 400 volt power supply. This reduces the startup current by a factor of 3.
To make the Y-D system work, we need a small control system - both for timing and performing the switch-over as well as assuring no short-circuit is possible. What should never-ever happen, is that the star and delta contactors close at the same time. This will essentially create a huge short-circuit - since we are actually simply connection the 3 phases together directly.
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