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# Relation Between Line Voltage And Phase Voltage In Star Connection Pdf

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## Three-phase A.C. Circuits

Three-phase electric power is a common method of alternating current electric power generation , transmission , and distribution.

It is also used to power large motors and other heavy loads. A three-wire three-phase circuit is usually more economical than an equivalent two-wire single-phase circuit at the same line to ground voltage because it uses less conductor material to transmit a given amount of electrical power.

The conductors between a voltage source and a load are called lines, and the voltage between any two lines is called line voltage. The voltage measured between any line and neutral is called phase voltage. In a symmetric three-phase power supply system, three conductors each carry an alternating current of the same frequency and voltage amplitude relative to a common reference but with a phase difference of one third of a cycle between each.

The common reference is usually connected to ground and often to a current-carrying conductor called the neutral. Due to the phase difference, the voltage on any conductor reaches its peak at one third of a cycle after one of the other conductors and one third of a cycle before the remaining conductor. This phase delay gives constant power transfer to a balanced linear load. It also makes it possible to produce a rotating magnetic field in an electric motor and generate other phase arrangements using transformers for instance, a two phase system using a Scott-T transformer.

The symmetric three-phase systems described here are simply referred to as three-phase systems because, although it is possible to design and implement asymmetric three-phase power systems i.

In a three-phase system feeding a balanced and linear load, the sum of the instantaneous currents of the three conductors is zero. In other words, the current in each conductor is equal in magnitude to the sum of the currents in the other two, but with the opposite sign. The return path for the current in any phase conductor is the other two phase conductors.

As compared to a single-phase AC power supply that uses two conductors phase and neutral , a three-phase supply with no neutral and the same phase-to-ground voltage and current capacity per phase can transmit three times as much power using just 1.

Thus, the ratio of capacity to conductor material is doubled. Constant power transfer and cancelling phase currents would in theory be possible with any number greater than one of phases, maintaining the capacity-to-conductor material ratio that is twice that of single-phase power. However, two-phase power results in a less smooth pulsating torque in a generator or motor making smooth power transfer a challenge , and more than three phases complicates infrastructure unnecessarily.

Three-phase systems may also have a fourth wire, particularly in low-voltage distribution. This is the neutral wire. The neutral allows three separate single-phase supplies to be provided at a constant voltage and is commonly used for supplying groups of domestic properties which are each single-phase loads.

The connections are arranged so that, as far as possible in each group, equal power is drawn from each phase. Further up the distribution system , the currents are usually well balanced. Transformers may be wired in a way that they have a four-wire secondary but a three-wire primary while allowing unbalanced loads and the associated secondary-side neutral currents. Three-phase supplies have properties that make them very desirable in electric power distribution systems:.

Most household loads are single-phase. In North American residences, three-phase power might feed a multiple-unit apartment block, but the household loads are connected only as single phase.

In lower-density areas, only a single phase might be used for distribution. Some high-power domestic appliances such as electric stoves and clothes dryers are powered by a split phase system at volts or from two phases of a three phase system at volts only.

Wiring for the three phases is typically identified by color codes which vary by country. Connection of the phases in the right order is required to ensure the intended direction of rotation of three-phase motors.

For example, pumps and fans may not work in reverse. Maintaining the identity of phases is required if there is any possibility two sources can be connected at the same time; a direct interconnection between two different phases is a short circuit. At the power station , an electrical generator converts mechanical power into a set of three AC electric currents , one from each coil or winding of the generator.

The generator frequency is typically 50 or 60 Hz , depending on the country. At the power station, transformers change the voltage from generators to a level suitable for transmission in order to minimize losses. After further voltage conversions in the transmission network, the voltage is finally transformed to the standard utilization before power is supplied to customers.

Most automotive alternators generate three-phase AC and rectify it to DC with a diode bridge. A "delta" connected transformer winding is connected between phases of a three-phase system. A "wye" transformer connects each winding from a phase wire to a common neutral point. In an "open delta" or "V" system, only two transformers are used. A closed delta made of three single-phase transformers can operate as an open delta if one of the transformers has failed or needs to be removed.

Where a delta-fed system must be grounded for detection of stray current to ground or protection from surge voltages, a grounding transformer usually a zigzag transformer may be connected to allow ground fault currents to return from any phase to ground. Another variation is a "corner grounded" delta system, which is a closed delta that is grounded at one of the junctions of transformers.

As shown in the diagram, a delta configuration requires only three wires for transmission but a wye star configuration may have a fourth wire. The fourth wire, if present, is provided as a neutral and is normally grounded. The three-wire and four-wire designations do not count the ground wire present above many transmission lines, which is solely for fault protection and does not carry current under normal use.

A four-wire system with symmetrical voltages between phase and neutral is obtained when the neutral is connected to the "common star point" of all supply windings. In such a system, all three phases will have the same magnitude of voltage relative to the neutral. Other non-symmetrical systems have been used. The four-wire wye system is used when a mixture of single-phase and three-phase loads are to be served, such as mixed lighting and motor loads.

An example of application is local distribution in Europe and elsewhere , where each customer may be only fed from one phase and the neutral which is common to the three phases.

When a group of customers sharing the neutral draw unequal phase currents, the common neutral wire carries the currents resulting from these imbalances. Electrical engineers try to design the three-phase power system for any one location so that the power drawn from each of three phases is the same, as far as possible at that site. Hence, every effort is made by supply authorities to distribute the power drawn on each of the three phases over a large number of premises so that, on average, as nearly as possible a balanced load is seen at the point of supply.

Generally, there are four different types of three-phase transformer winding connections for transmission and distribution purposes.

In North America, a high-leg delta supply is sometimes used where one winding of a delta-connected transformer feeding the load is center-tapped and that center tap is grounded and connected as a neutral as shown in the second diagram. The reason for providing the delta connected supply is usually to power large motors requiring a rotating field.

In the perfectly balanced case all three lines share equivalent loads. Examining the circuits we can derive relationships between line voltage and current, and load voltage and current for wye and delta connected loads. In a balanced system each line will produce equal voltage magnitudes at phase angles equally spaced from each other.

With V 1 as our reference and V 3 lagging V 2 lagging V 1 , using angle notation , and V LN the voltage between the line and the neutral we have: [14]. The voltage seen by the load will depend on the load connection; for the wye case, connecting each load to a phase line-to-neutral voltages gives: [14]. The phase angle difference between voltage and current of each phase is not necessarily 0 and is dependent on the type of load impedance, Z y.

Inductive and capacitive loads will cause current to either lag or lead the voltage. By applying Kirchhoff's current law KCL to the neutral node, the three phase currents sum to the total current in the neutral line. In the balanced case:. In the delta circuit, loads are connected across the lines, and so loads see line-to-line voltages: [14].

Calculating line currents by using KCL at each delta node gives:. Except in a high-leg delta system, single-phase loads may be connected across any two phases, or a load can be connected from phase to neutral. In a symmetrical three-phase four-wire, wye system, the three phase conductors have the same voltage to the system neutral.

The currents returning from the customers' premises to the supply transformer all share the neutral wire. If the loads are evenly distributed on all three phases, the sum of the returning currents in the neutral wire is approximately zero.

Any unbalanced phase loading on the secondary side of the transformer will use the transformer capacity inefficiently. If the supply neutral is broken, phase-to-neutral voltage is no longer maintained. Phases with higher relative loading will experience reduced voltage, and phases with lower relative loading will experience elevated voltage, up to the phase-to-phase voltage.

The method of symmetrical components is used to analyze unbalanced systems. With linear loads, the neutral only carries the current due to imbalance between the phases. Gas-discharge lamps and devices that utilize rectifier-capacitor front-end such as switch-mode power supplies , computers, office equipment and such produce third-order harmonics that are in-phase on all the supply phases.

Consequently, such harmonic currents add in the neutral in a wye system or in the grounded zigzag transformer in a delta system , which can cause the neutral current to exceed the phase current. An important class of three-phase load is the electric motor. A three-phase induction motor has a simple design, inherently high starting torque and high efficiency. Such motors are applied in industry for many applications. Three-phase motors also vibrate less and hence last longer than single-phase motors of the same power used under the same conditions.

Resistance heating loads such as electric boilers or space heating may be connected to three-phase systems. Electric lighting may also be similarly connected. Line frequency flicker in light is detrimental to high speed cameras used in sports event broadcasting for slow motion replays. It can be reduced by evenly spreading line frequency operated light sources across the three phases so that the illuminated area is lit from all three phases.

This technique was applied successfully at the Beijing Olympics. Rectifiers may use a three-phase source to produce a six-pulse DC output.

Such rectifiers may be used for battery charging, electrolysis processes such as aluminium production or for operation of DC motors.

One example of a three-phase load is the electric arc furnace used in steelmaking and in refining of ores. In many European countries electric stoves are usually designed for a three-phase feed.

Individual heating units are often connected between phase and neutral to allow for connection to a single-phase circuit if three-phase is not available. Most groups of houses are fed from a three-phase street transformer so that individual premises with above-average demand can be fed with a second or third phase connection. Phase converters are used when three-phase equipment needs to be operated on a single-phase power source. They are used when three-phase power is not available or cost is not justifiable.

Such converters may also allow the frequency to be varied, allowing speed control. Some railway locomotives use a single-phase source to drive three-phase motors fed through an electronic drive.

## Three-phase electric power

Orders delivered to U. Learn more. If the three-phase loads are balanced each having equal impedances , the analysis of such a circuit can be simplified on a per-phase basis. This follows from the relationship that the per-phase real power and reactive power are one-third of the total real power and reactive power, respectively. It is very convenient to carry out the calculations in a per-phase star-connected line to neutral basis. Two three-phase load connections that are commonly used in the ac circuits were given in Fig.

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. The Effect of Delta and Star Connections upon Transformer Wave Forms Abstract: The purpose of the paper is to show the distortions resulting from different symmetrical three-phase connections of generator and transformers without transmission line, as dependent upon the hysteresis cycle and the admittance of the transformers at no-load. Tests were made with the oscillograph to show the no-load exciting current and voltage waves of three single-phase step-up transformers when the windings of the generator and both sides of the transformers were connected in all possible symmetrical delta and star relations.

## Three Phase Transformer Connections

Three-phase electric power is a common method of alternating current electric power generation , transmission , and distribution. It is also used to power large motors and other heavy loads. A three-wire three-phase circuit is usually more economical than an equivalent two-wire single-phase circuit at the same line to ground voltage because it uses less conductor material to transmit a given amount of electrical power. The conductors between a voltage source and a load are called lines, and the voltage between any two lines is called line voltage. The voltage measured between any line and neutral is called phase voltage.

Table of Contents. In Star also denoted by Y system of interconnection, the starting ends or finishing ends similar ends of three coils are connected together to form the neutral point.

### Three-phase Y and Delta Configurations

This configuration of voltage sources is characterized by a common connection point joining one side of each source. Figure below. The three conductors leading away from the voltage sources windings toward a load are typically called lines , while the windings themselves are typically called phases. In a Y-connected system, there may or may not Figure below be a neutral wire attached at the junction point in the middle, although it certainly helps alleviate potential problems should one element of a three-phase load fail open, as discussed earlier. Line voltage refers to the amount of voltage measured between any two line conductors in a balanced three-phase system.

In the Star Connection , the similar ends either start or finish of the three windings are connected to a common point called star or neutral point. The three-line conductors run from the remaining three free terminals called line conductors. The wires are carried to the external circuit, giving three-phase, three-wire star connected systems. However, sometimes a fourth wire is carried from the star point to the external circuit, called neutral wire , forming three-phase, four-wire star connected systems. Considering the above figure, the finish terminals a 2 , b 2 , and c 2 of the three windings are connected to form a star or neutral point. The three conductors named as R, Y and B run from the remaining three free terminals as shown in the above figure.

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To derive the relations between line and phase currents and voltages of a star connected system, we have first to draw a balanced star.

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