Chapter 15. Transformer Connections
10 Pages

Chapter 15. Transformer Connections

Course: ENGINEERIN ELEC121, Spring 2010

School: University of Liverpool

Word Count: 4870

Rating:

Document Preview

15 Transformer Connections 15.1 15.2 15.3 15.4 Introduction..................................................................... 15-1 Polarity of Single-Phase Transformers........................... 15-1 Angular Displacement of Three-Phase Transformers .................................................................... 15-2 Three-Phase Transformer Connections ......................... 15-2 Double-Wound...

Unformatted Document Excerpt
Coursehero >> United Kingdom >> University of Liverpool >> ENGINEERIN ELEC121

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Connections 15.1 15 Transformer 15.2 15.3 15.4 Introduction..................................................................... 15-1 Polarity of Single-Phase Transformers........................... 15-1 Angular Displacement of Three-Phase Transformers .................................................................... 15-2 Three-Phase Transformer Connections ......................... 15-2 Double-Wound Transformers . Multiwinding Transformers Autotransformers Connections . Interconnected-Wye and Grounding Transformers . Phase-Shifting Transformers . Dan D. Perco Perco Transformer Engineering 15.5 15.6 Three-Phase to Six-Phase Connections....................... 15-10 Paralleling of Transformers........................................... 15-10 15.1 Introduction In deciding the transformer connections required in a particular application, there are so many considerations to be taken into account that the nal solution must necessarily be a compromise. It is therefore necessary to study in detail the various features of the transformer connections together with the local requirements under which the transformer will be operated. The advantages and disadvantages of each type of connection should be understood and taken into consideration. This section describes the common connections for distribution, power, HVDC (high-voltage dc) converter, rectier, and phase-shifting transformers. Space does not permit a detailed discussion of other uncommon transformer connections. The information presented in this section is primarily directed to transformer users. Additional information can be obtained from the IEEE transformer standards. In particular, reference is made to IEEE Std. C57.12.70, Terminal Markings and Connections for Distribution and Power Transformers; C57.105, Application of Transformer Connections in Three-Phase Distribution Systems; C57.129, General Requirements and Test Code for Oil-Immersed HVDC Converter Transformers; C57.18.10, Practices and Requirements for Semiconductor Power and Rectier Transformers; C57.12.20, Overhead-Type Distribution Transformers; and C57.135, IEEE Guide for the Application, Specication, and Testing of Phase-Shifting Transformers. 15.2 Polarity of Single-Phase Transformers The term polarity as applied to transformers is used to indicate the phase relationship between the primary and secondary windings of a given transformer or to indicate the instantaneous relative direction of voltage phasors in the windings of different transformers. This facilitates rapid and accurate connections of transformers in service. Transformer manufacturers have agreed to standardize the marking of terminals 2006 by Taylor & Francis Group, LLC. to indicate their polarity. For a single-phase, two-winding transformer, the high-voltage terminals are labeled H1 and H2, while the lowH1 H2 H1 H2 voltage terminals are labeled X1 and X2. When transformers are to be operated in parallel, likemarked terminals are to be joined together. Transformers can be either subtractive or additive polarity. When like-numbered terminals such as H1 and X1 are joined together, the voltage between the other open terminals will be the difference of the individual X1 X2 X2 X1 impressed winding voltages for a transformer with subtractive polarity. For additive-polarity FIGURE 15.1 Single-phase transformer-terminal markings. transformers, the voltage between the open terminals will be the sum of the individual winding voltages. The standards specify subtractive polarity for all transformers except for single-phase transformers 200 kVA and smaller and having high-voltage windings 8660 volts and below. In either case, the polarity of the transformer is identied by the terminal markings as shown in Figure 15.1. Subtractive polarity has correspondingly marked terminals for the primary and secondary windings opposite each other. For additive polarity, like-numbered winding terminal markings are diagonally disposed. Transformers with subtractive polarity normally have the primary and secondary windings wound around the core in the same direction. However, the transformer can have subtractive-polarity terminal markings with the primary and secondary coils wound in the opposite directions if the internal winding leads are reversed. Subtractive polarity Additive polarity 15.3 Angular Displacement of Three-Phase Transformers Angular displacement is dened as the phase angle in degrees between the line-to-neutral voltage of the reference-identied high-voltage terminal and the line-to-neutral voltage of the corresponding identied low-voltage terminal. The angle is positive when the low-voltage terminal lags the high-voltage terminal. The convention for the direction of rotation of the voltage phasors is taken as counterclockwise. Since the bulk of the electric power generated and transmitted is three-phase, the grouping of transformers for three-phase transformations is of the greatest interest. Connection of three-phase transformers or three single-phase transformers in a three-phase bank can create angular displacement between the primary and secondary terminals. The standard angular displacement for two-winding transformers is shown in Figure 15.2. The references for the angular displacement are shown as dashed lines. The angular displacement is the angle between the lines drawn from the neutral to H1 and from the neutral to X1 in a clockwise direction from H1 to X1. The angular displacement between the primary and secondary terminals can be changed from 08 to 3308 in 308 steps simply by altering the three-phase connections of the transformer. Therefore, selecting the appropriate three-phase transformer connections will permit connection of systems with different angular displacements. Figure 15.2 shows angular displacement for common double-wound three-phase transformers. Multicircuit and autotransformers are similarly connected. 15.4 Three-Phase Transformer Connections Three-phase connections can be made either by using three single-phase transformers or by using a three-phase transformer. Advantages of the three-phase transformer is that it costs less, the weight is less, it requires less oor space, and has lower losses than three single-phase transformers. Circuit computations involving three-phase transformer banks under balanced conditions can be made by dealing with 2006 by Taylor & Francis Group, LLC. Group 1 Angular Displacement 0 H2 DELTA-DELTA H1 H2 DELTA-ZIGZAG H1 H2 STAR-STAR H1 H2 ZIGZAG-DELTA H1 H3 X1 X3 H1 X1 X2 H3 X1 X2 X3 H1 H3 X1 X2 X3 H1 X2 Group 2 Angular Displacement 30 H2 DELTA-STAR X1 H3 H2 ZIGZAG-STAR X1 H3 H2 STAR-DELTA X1 X3 H1 H2 STAR-ZIGZAG X1 H3 H3 X3 X2 X3 X2 X3 X2 X2 H3 X3 FIGURE 15.2 Standard angular displacement for three-phase transformers. only one of the transformers or phases. It is more convenient to use line-to-neutral values, since transformer impedances can then be added directly to transmission-line impedances. All impedances must be converted to the same side of the transformer bank by multiplying them by the square of the voltage ratio. There are two basic types of three-phase transformers, core type and shell type. The magnetic circuit of the shell type is very similar to three single-phase transformers. This type of transformer has a return circuit for each phase of the magnetic ux. Consequently, the zero-sequence impedance is equal to the positivesequence impedance. The conditions with respect to magnetizing currents and zero-sequence impedances are essentially the same as for single-phase transformers connected in the same way. The center-phase coil is usually wound in a direction opposite to that of the two outer phases in order to decrease the core yoke required between phases. This reversal of polarity is corrected when the leads are terminated. The magnetic circuit of each phase of a three-limb core-type transformer is mutually connected in that the ux of one phase must return through the other two phases. In this type of transformer, the total instantaneous magnetic ux in each core section due to the fundamental excitation current is zero. However, in the wyewye-connected transformer, there are third-harmonic voltages in the phases caused by the third-harmonic current. These voltages and the resulting magnetic ux are all induced in the same direction. Since there is no return path for this ux in the core, the ux must return through the relatively low-reluctance path outside the core. The core-type transformer is occasionally manufactured with a ve-limb core. In this case, the magnetic circuit and performance characteristics are similar to that of shell-type or single-phase transformers. Unbalanced system faults and loads can cause signicant zero-sequence magnetic ux to occur for some three-phase connections. Unless a magnetic return path for this ux is provided, the ux returns outside the core and can cause eddy-current heating in other transformer conductive components, such as the tank. The existence of zero-sequence ux either within or outside the core depends on both core conguration and winding connections. Three-phase transformer-core assemblies do not usually provide full-capacity return legs for zero-sequence ux. Thus, if sufcient zero-sequence ux occurs, it will be forced to return outside the core. 2006 by Taylor & Francis Group, LLC. Three-phase transformer connections can be compared with each other with respect to: . . . . . . Ratio of kVA output to the kVA internal rating of the bank Degree of voltage symmetry with unbalanced phase loads Voltage and current harmonics Transformer ground availability System fault-current level Switching and system fault and transient voltages In some cases, there may also be other operating characteristics to determine the most suitable connection for each application. 15.4.1 Double-Wound Transformers The majority of three-phase transformer connections are made by connecting the individual phases either between the power-system lines, thus forming a delta connection, or by connecting one end of each phase together and the other ends to the lines, thus forming a wye (also referred to as star) connection. For these connections, the total rating of the internal windings is equal to the through-load rating. This accounts for the popularity of these connections. For all other double-wound transformer connections, the ratio is less than unity. For example, in the interconnected star or zigzag connection, the transformer is capable of delivering a load equal to only 86.6% of the internal winding rating. Since the cost of a transformer varies approximately with the three-quarter power of the internal kVA, the cost of an interconnected star or zigzag transformer is approximately 5% higher than for a similar double-wound transformer. All of these types of three-phase connections are shown in Figure 15.2. 15.4.1.1 Wye-Wye Connections of Transformers Joining together the terminals of similar windings with the same polarity derives the neutral of the wye connection. This neutral point is available and can be brought out for any desired purpose, such as grounding or zero-sequence current measurements and protection. For high-voltage transmission systems, the use of the wye-connected transformer is more economical because the voltage across the phase of each winding is a factor of 1.73 less than the voltage between the lines. If the neutral point is grounded, it is not necessary to insulate it for the line voltage. If the neutral is not grounded, the fault current during a system line to ground fault is insignicant because of the absence of a zero-sequence current path. If the neutral is grounded in the wyewye transformer and the transformer is made with a three-limb core, the zero-sequence impedance is still high. As a result, the fault currents during a system line-to-ground fault are relatively low. For wyewye transformers made of three single-phase units or with a shell-type or ve-limb core-type, the zerosequence impedance is approximately equal to the positive-sequence impedance. The fault current during a system ground fault for this case is usually the limiting factor in the design of the transformer. In all types of wye-wye transformer connections, only the transformer positive-sequence impedance limits the fault current during a system three-phase system fault. With the wye connection, the voltages are symmetrical as far as the lines are concerned, but they introduce third-harmonic (or multiples of the third harmonic) voltage and current dissymmetry between lines and neutral. The third-harmonic voltage is a zero-sequence phenomenon and thereby is exhibited in the same direction on all phases. If the transformer and generator neutrals are grounded, third-harmonic currents will ow that can create interference in telephone circuits. If the transformer neutral is not grounded, the third-harmonic voltage at the neutral point will be additive for all three phases, and the neutral voltage will oscillate around the zero point at three times the system frequency. Third-harmonic voltages are also created on the lines, which can subject the power system to dangerous overvoltages due to resonance with the line capacitance. This is particularly true for shelltype three-phase transformers, ve-limb core-type transformers, and three-phase banks of single-phase transformers. For any three-phase connection of three-limb core-form transformers, the impedance to 2006 by Taylor & Francis Group, LLC. third-harmonic ux is relatively high on account of the magnetic coupling between the three phases, resulting in a more stabilized neutral voltage. A delta tertiary winding can be added on wyewye transformers to provide a path for third-harmonic and zero-sequence currents and to stabilize the neutral voltage. The tertiary in this application will be required to carry all of the zero-sequence fault current during a system line-to-ground fault. The most common way to supply unbalanced loads is to use a four-wire wye-connected circuit. However, the primary windings of the transformer bank cannot be wye-connected unless the primary neutral is joined to the neutral of the generator. In this case, a third-harmonic voltage exists from each secondary line-to-neutral voltage because the generator supplies a sinusoidal excitation current. The third-harmonic currents created by the third-harmonic voltages can be a source of telephone interference. If the primary neutral is not connected to the generator, single-phase or unbalanced three-phase loads in the secondary cannot be supplied, since the primary current has to ow through the high impedance of the other primary windings. 15.4.1.2 DeltaDelta Connection The deltadelta connection has an economic advantage over the wyewye connection for low-voltage, high-current requirements because the winding current is reduced by a factor of 1.73 to 58% of that in the wyewye connection. Voltage and current symmetry with respect to the three lines is obtained only in the delta and zigzag connections. Delta-connected transformers do not introduce third harmonics or their multiples into the power lines. The third-harmonic-induced voltage components are 3608 apart. They are therefore all in phase and cause a third-harmonic current to ow within the delta winding. This third-harmonic current acts as exciting current and causes a third-harmonic voltage to be induced in each winding that is in opposition to the third-harmonic component of voltage that was originally induced by the sinusoidal exciting current from the lines. As a result, the third harmonic is eliminated from the secondary voltage. Another advantage of the deltadelta connection, if composed of three single-phase transformers, is that one transformer can be removed and the remaining two phases operated at 86.6% of their rating in the open delta connection. The principle disadvantage of the deltadelta connection is that the neutral is not available. As a result, the phases cannot be grounded except at the corners. The insulation design is more costly because this type of three-phase transformer connection has higher ground voltages during system fault or transient voltages. Supplying an articial neutral to the system with a grounding transformer can help to control these voltages. The delta-connection insulation costs increase with increasing voltage. Consequently, this type of connection is commonly limited to a maximum system voltage of 345 kV. Differences in the voltage ratio of the individual phases a causes circulating current in both the primary and secondary deltas that is limited only by the impedance of the units. Differences in the impedances of the individual phases also causes unequal load division among the phases. When a current is drawn from the terminals of one phase of the secondary, it ows in the windings of all three phases. The current among the phases divides inversely with the impedance of the parallel paths between the terminals. 15.4.1.3 DeltaWye and WyeDelta Connections The deltawye or wyedelta connections have fewer objectionable features than any other connections. In general, these combine most of the advantages of the wyewye and deltadelta connections. Complete voltage and current symmetry is maintained by the presence of the delta. The exciting third-harmonic current circulates within the delta winding, and no third-harmonic voltage appears in the phase voltages on the wye side. The high-voltage windings can be connected wye, and the neutral can be brought out for grounding to minimize the cost of the insulation. Differences in magnetizing current, voltage ratio, or impedance between the single-phase units are adjusted by a small circulating current in the delta. All of these factors result in unbalanced phase voltages on the delta, which causes a current to circulate within the delta. 2006 by Taylor & Francis Group, LLC. If the primary windings of a four-wire, wye-connected secondary that is supplying unbalanced loads are connected in delta, the unbalanced loading can be readily accommodated. There will be unbalanced secondary voltages caused by the difference in the regulation in each phase, but this is usually insignicant. Although the deltawye connection has most of the advantages of the wyewye and deltadelta, it still has several disadvantages. This connection introduces a 308 phase shift between the primary and secondary windings that has to be matched for paralleling. A deltawye bank cannot be operated with only two phases in an emergency. If the delta is on the primary side and should accidentally open, the unexcited leg on the wye side can resonate with the line capacitance. 15.4.2 Multiwinding Transformers Transformers having more than two windings coupled to the same core are frequently used in power and distribution systems to interconnect three or more circuits with different voltages or to electrically isolate two or more secondary circuits. For these purposes, a multiwinding transformer is less costly and more efcient than an equivalent number of two winding transformers. The arrangement of windings can be varied to change the leakage reactance between winding pairs. In this way, the voltage regulation and the short-circuit requirements are optimized. The application of multiwinding transformers permits: . . . . . . . Interconnection of several power systems operating at different voltages Use of a delta-connected stabilizing winding, which can also be used to supply external loads Control of voltage regulation and reactive power Electrical isolation of secondary circuits Duplication of supply to a critical load Connection for harmonic-ltering equipment A source for auxiliary power at a substation Some of the problems with the use of multiwinding transformers are associated with the effect leakage impedance has on voltage regulation, short-circuit currents, and the division of load among the different circuits. All the windings are magnetically coupled to the leakage ux and are affected by the loading of the other windings. It is therefore essential to understand the leakage impedance behavior of this type of transformer to be able to calculate the voltage regulation of each winding and load sharing among the windings. For three-winding transformers, the leakage reactance between each pair of windings must be converted into a star-equivalent circuit. The impedance of each branch of the star circuit is calculated as follows: Za 0:5(Zab Zca Zbc ) Zb 0:5(Zbc Zab Zca ) and Zc 0:5(Zca Zbc Zab ) (15:3) (15:1) (15:2) where Za, Zb, and Zc are the star-equivalent impedances in each branch Zab, Zbc, and Zca are the impedances as seen from the terminals between each pair of windings with the remaining winding left open circuit The equivalent star-circuit reactances and resistances are determined in the same manner. The four-winding transformer coupled to the same core is not commonly used because of the interdependence of the voltage regulation of each winding to the loading on the other windings. The 2006 by Taylor & Francis Group, LLC. equivalent circuit for a four-winding transformer is much more complicated, involving a complex circuit of six different impedances. After the loading of each winding is determined, the voltage regulation and load sharing can be calculated for each impedance branch and between terminals of different windings. The currents in each winding during a system fault can also be calculated in a similar fashion. 15.4.3 Autotransformers Connections It makes no difference whether the secondary voltage is obtained from another coil or from the primary turns. The same transformation ratio is obtained in either case. When the primary and secondary voltages are obtained from the same coil, schematically, the transformer is called an autotransformer. The performance of autotransformers is governed by the same fundamental considerations as for transformers with separate windings. The autotransformer not only requires less turns than the two-winding transformer; it also requires less conductor cross section in the common winding because it has to carry only the differential current between the primary and secondary. As a result, autotransformers deliver more external load than the internal-winding kVA ratings, depending on the voltage ratios of the primary and secondary voltages, as shown in Figure 15.3 and the following formula: Output=internal rating V1 =(V1 V2 ) where V1 voltage of the higher-voltage winding V2 voltage of the lower-voltage winding The internal rating, size, cost, excitation current, and efciency of autotransformers are higher than in double-wound transformers. The greatest benet of the autotransformer is achieved when the primary and secondary voltages are close to each other. A disadvantage of the autotransformer is that the short-circuit current and forces are increased because of the reduced leakage reactance. In addition, most three-phase autotransformers are wye wye connected. This form of connection has the same limitations as for the wyewye double-wound transformers. Furthermore, there is no electrical isolation between the primary and secondary circuits with an autotransformer connection. An autotransformer often has a delta-connected tertiary winding to reduce third-harmonic voltages, to permit the transformation of unbalanced three-phase loads, and to enable the use of supply-station auxiliary load or power-factor improvement equipment. The tertiary winding must be designed to Line V1 I1 Primary I1 I2 V2 I2 X Load I2 I2 X Load V2 I2 Secondary I1 I1 a Common I2 I1 b V1 Series I1 I1 c (15:4) FIGURE 15.3 Current ow in double-wound transformer and autotransformer. 2006 by Taylor & Francis Group, LLC. accept all of these external loads as well as the severe short-circuit currents and forces associated with three-phase faults on its own terminals or single line-to-ground faults on either the primary or secondary terminals. If no external loading is required, the tertiary winding terminals should not be brought out except for one terminal to ground one corner of the delta during service operation. This eliminates the possibility of a three-phase external fault on the winding. The problem of transformer insulation stresses and system transient protection is more complicated for autotransformers, particularly when tapping windings are also required. Transient voltages can also be more easily transferred between the power systems with the autotransformer connection. 15.4.4 Interconnected-Wye and Grounding Transformers The interconnected-wye-wye connections have the advantages of the stardelta connections with the additional advantage of the neutral. The interconnected-wye or zigzag connection allows unbalancedphase load currents without creating severe neutral voltages. This connection also provides a path for third-harmonic currents created by the nonlinearity of the magnetic core material. As a result, interconnected-wye neutral voltages are essentially eliminated. However, the zero-sequence impedance of interconnected-wye windings is often so low that high third-harmonic and zero-sequence currents will result when the neutral is directly grounded. These currents can be limited to an acceptable level by connecting a reactor between the neutral and ground. The interconnected-wye-wye connection has the disadvantage that it requires 8% additional internal kVA capacity. This and the additional complexity of the leads make this type of transformer connection more costly than the other common types discussed above. The stable neutral inherent in the interconnected-wye or zigzag connection has made its use possible as a grounding transformer for systems that would be isolated otherwise. This is shown in Figure 15.4. The connections to the second set of windings can be reversed to produce the winding angular displacements shown in Figure 15.2. For a line-to-neutral load or a line-to-ground fault on the system, the current is limited by the leakage reactance between the two coils on each phase of the grounding transformer. 15.4.5 Phase-Shifting Transformers The development of large, high-voltage power grids has increased the reliability and efciency of electric power systems. However, the difference of voltages, impedance, loads, and phase angles between paralleled power lines causes unbalanced line-loading. The phase-shifting transformer is used to provide a phase shift between two systems to control the power ow. A phase-shifting transformer (PST) is a transformer that advances or retards the voltage phase-angle relationship of one circuit with respect to H2 H1 H2 H3 b1 a1 a2 b1 b2 c1 c2 c2 a2 c1 b2 H1 (a) (b) a1 H3 FIGURE 15.4 Interconnected star-grounding transformer: (a) current distribution in the coils for a line-to-ground fault and (b) normal operating voltages in the coils. 2006 by Taylor & Francis Group, LLC. another circuit. In some cases, phase-shifting transformers can also control the reactive power ow by varying the voltages between the two circuits. There are numerous different circuits and transformer designs used for this application. The two main type of PSTs used are shown in Figure 15.5a and Figure 15.5b. The single-core design shown in Figure 15.5a is most commonly used. With this design, it is generally accepted practice to provide two sets of three single-pole tap changers: one set on the source terminals and one set on the load terminals. This permits symmetrical voltage conditions while varying the phase angle from maximum advance to maximum retard tap positions. If only one set of three single-pole tap changers is used, the load voltage varies as the tap-changer phase-shift position is varied. The single-core design is less complicated, has less internal kVA, and is less costly than the other designs used. However, it has the following disadvantages: . . . The LTC and tap windings are at the line ends of the power systems and are directly exposed to system transient voltages. The impedance of the PST varies directly with the square of the number of tap positions away from the mid-tap position. The impedance of this type of PST at the mid-tap or zero-phase-shift position is negligible. As a result, the short-circuit current at or near the mid-tap position is limited only by the system impedance. The maximum capacity of this type of PST is generally limited by the maximum voltage or current limitation of the tap changers. As a result, the maximum switching capacity of the tap V1 S IS1 L IL1 VL1 V10 V VS1 1 V10 V20 V30 V30 (a) S1 S2 S3 IL1 ~ ~ ~ ~ ~~ ~ ~ I IS1 V20 L1 L2 L3 VL1 VS1 VS3 VL3 VS2 VL2 Advanced position (b) Series unit Main unit FIGURE 15.5 Two main type of PSTs: (a) single core; (b) dual core. 2006 by Taylor & Francis Group, LLC. . . changer cannot be fully utilized. The space required by these tap changers cause shipping restrictions in large-capacity PSTs. The transient voltage on the tap-changer reversing switch when switching through the mid-point position is very high. Usually, additional components are required in the PST or tap changer to limit these transfer voltages to an acceptable level. The cost of single-pole tap changers is substantially higher than three-pole tap changers used with some of the other PST designs. The other common PST circuit used is shown in Figure 15.5b. This PST design requires two separate cores, one for the series unit and one for the main or excitation unit. For large power, this PST design requires two separate tanks with oil-lled throat connection between them. This type of design does not have the technical limitations of the single-core design. Furthermore, another tap winding connected in quadrature to the phase-shifting tap windings can be readily added to provide voltage regulation as well as phase-shift control. This enables essentially independent control of the real and reactive power ow between the systems. However, the cost of this type of PST design is substantially higher because of the additional core, windings, and internal kVA capacity required. 15.5 Three-Phase to Six-Phase Connections The three-phase connections discussed above are commonly used for six-pulse rectier systems. However, for 12-pulse rectier systems, three-phase to six-phase transformations are required. For low-voltage dc applications, there are numerous practical connection arrangements possible to achieve this. However, for high-voltage dc (HVDC) applications, there are few practical arrangements. The most commonly used connections are either a delta or wye primary with two secondaries: one wye- and one delta-connected. 15.6 Paralleling of Transformers Transformers having terminals marked in the manner shown in Section 15.2, polarity of Single-Phase Transformers, can be operated in parallel by connecting similarly marked terminals provided that their ratios, voltages, angular displacement, resistances, reactances, and ground connections are such as to permit parallel operation. The difference in the no-load terminal voltages of the transformers causes a circulating current to ow between the transformers when paralleled. This current ows at any load. The impedance of the circuit, which is usually the sum of the impedances of the transformers that are operating in parallel, limits the circulating current. The inductive circulating current adds, considering proper phasor relationships, to the load current to establish the total current in the transformer. As a result, the capacity of the transformer to carry load current is reduced by the circulating current when the transformers are paralleled. For voltage ratios with a deviation of less than the 0.5%, as required by the IEEE standards, the circulating current between paralleled transformers is usually insignicant. The load currents in the paralleled transformers divide inversely with the impedances of the paralleled transformers. Generally, the difference in resistance has an insignicant effect on the circulating current because the leakage reactance of the transformers involved is much larger than the resistance. Transformers with different impedance values can be made to divide their load in proportion to their load ratings by placing a reactor in series with one transformer so that the resultant impedance of the two branches creates the required load sharing. When deltadelta connected transformer banks are paralleled, the voltages are completely determined by the external circuit, but the division of current among the phases depends on the internal characteristics of the transformers. Considerable care must be taken in the selection of transformers, particularly single-phase transformers in three-phase banks, if the full capacity of the banks is to be used when the ratios of transformation on all phases are not alike. In the deltawye connection, the division of current is indifferent to the differences in the characteristics of individual transformers. 2006 by Taylor & Francis Group, LLC.

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

University of Liverpool - ENGINEERIN - ELEC121
13Load Tap Changers13.1 13.2 13.3 13.4 13.5 13.6 13.7 Introduction. 13-1 Switching Principle . 13-2 Design Concepts of Todays Load Tap Changers . 13-3Oil-Type Load Tap Changers . Vacuum-Type Load Tap Changers . Tap Position IndicationApplications of L
University of Liverpool - ENGINEERIN - ELEC121
16Transformer Testing16.1 16.2 16.3 16.4 16.5 16.6 Introduction. 16-1Standards . Classication of Tests Scope of This Chapter.Sequence of Tests.Voltage Ratio and Proper Connections . 16-4The Purpose of Ratio, Polarity, and Phase-Relation Tests . Ra
University of Liverpool - ENGINEERIN - ELEC121
17Load-Tap-Change Control and Transformer Paralleling17.1 17.2 17.3 17.4 17.5 17.6 Introduction. 17-1 System Perspective, Single Transformer . 17-2 Control Inputs . 17-3Voltage Input . Current Input and Current Inputs.Phasing of VoltageThe Need for
University of Liverpool - ENGINEERIN - ELEC121
18Power Transformer Protection18.1 18.2 18.3 Introduction . 18-1 Transformer Differential Protection . 18-2 Magnetizing Inrush, Overexcitation, and CT Saturation . 18-4Inrush Currents CT Saturation.Transformer Overexcitation.18.4Methods for Discri
University of Liverpool - ENGINEERIN - ELEC121
19Causes and Effects of Transformer Sound Levels19.1 Transformer Sound Levels . 19-1Sound Pressure Level . Perceived Loudness . Sound Power . Sound Intensity Level . Relationship between Sound Intensity and Sound Pressure Level19.2 19.3 19.4Sound-Ene
University of Liverpool - ENGINEERIN - ELEC121
20Transient-Voltage Response20.1 Transient-Voltage Concerns. 20-1Normal System Operation . Sources and Types of Transient-Voltage Excitation . Addressing Transient-Voltage Performance . Complex Issue to Predict20.2Surges in Windings . 20-3Response o
University of Liverpool - ENGINEERIN - ELEC121
21Transformer Installation and Maintenance21.1 Transformer Installation . 21-1Receiving Inspection . Bushings . Oil Conservators . Gas Monitoring and Piping . Radiators . Coolers . Load Tap Changers (LTC) . Positive Pressure System . Control Cabinet .
University of Liverpool - ENGINEERIN - ELEC121
22Problem and Failure Investigation22.1 22.2 22.3 22.4 22.5 Introduction . 22-1 Background Investigation . 22-2Transformer Records . Transformer Protection Recording Devices . Operational History Transformer Components Dismantling Process. .Problem A
University of Liverpool - ENGINEERIN - ELEC121
23On-Line Monitoring of Liquid-Immersed Transformers23.1 23.2 23.3 Benets . 23-1Categories.Direct Benets.Strategic BenetsOn-Line Monitoring Systems. 23-3Sensors . Data-Acquisition Units . DAU-to-Computer Communications Line . Computer . Data Proc
Oregon State - CHEM - 201
Chemistry 201 Final ExamFall 2009 December 9Oregon State University DrapelaDO NOT OPEN THIS EXAM UNTIL INSTRUCTEDInstructions: 1. Fill in the front page of the Scantron answer sheet with your last name, first name, and middle initial. Fill in the circ
Oregon State - CHEM - 201
Oregon State - CHEM - 201
Oregon State - CHEM - 201
Oregon State - MATH - 254/255
Oregon State - CHEM - 201
CH 201 General Chemistry for Engineering MajorsDrapelaWelcome to ChemistryInstructor: Dr. Nicholas Drapela, Gilbert 231 Meeting times Tues,Thurs 80 minutesSections 8am 001 10am 003 Noon 002SyllabusThe complete syllabus is online at Blackboard; s
Oregon State - CHEM - 201
CH 201Tuesday, October 13 Ionic Formulas and NamesLast TimeTips for factor-label problems Convertingratios Units with exponents Atomic Structure Groups of elements Metals and nonmetals Formation of molecular compounds and ionic compoundsReview Que
Oregon State - CHEM - 201
CH 201Thursday, October 15 The MoleAnnouncement World premiere of Not Evil Just Wrong This Sunday, October 18 7pm, Milam Auditorium, OSU campus Free of charge Extra credit for CH 201 available Pickup question sheet if interestedMark your calendarR
Oregon State - CHEM - 201
CH 201 Chemistry For Engineering Majors Fall 2009Dr. Nick Drapela Office: 231 Gilbert Hall nick.drapela@orst.edu Office hours: W 10-11am W 2-3pmI. Required Course Materials- Masterton, Hurley Chemistry: Principles and Reactions, 6th Edition, Brooks/Col
Oregon State - CHEM - 201
INTRO TO COMPUTER SCIENCE I (CS_161_001_W2010) (CS_161_001_W2010) > ASSIGNMENTS > REVIEW ASSESSMENT: BLACKBOARD QUIZ/WORKSHEET 4Review Assessment: BlackboardQuiz/Worksheet 4Matthew T Cook 1/26/10 11:53 AM Blackboard Quiz/Worksheet 4 Completed 70 out of
Oregon State - CHEM - 201
Midterm 1 Study GuideLook over the Practice Exam at the top of our Announcement page for weeks 1-4. Read the Comments carefully so that you understand WHY. Look over your BBWS 1-4. Go to Blackboard -> Tools -> My Grades and click on a Blackboard quiz sco
Oregon State - CHEM - 201
Lab #8 Pre-lab Name _Matthew Cook1. Write a class header for a public class named Gui. The Gui class must be a child class of a class named JFrame. Public class Gui extends JFrame2. Go to the Java API and look up JButton. What is its parent class?Abstr
Oregon State - CHEM - 201
Lab #10 Pre-lab Name _1. Take a look at the tekpet API which is here: http:/web.engr.oregonstate.edu/~goskab/javadoc/ What exception can be thrown by turnOnLed() (in the Led class)?NotConnectedException2. Assume you have an Led object named bright. Wri
Oregon State - CHEM - 201
INTRO TO COMPUTER SCIENCE I (CS_161_001_W2010) (CS_161_001_W2010) > ASSIGNMENTS > REVIEW ASSESSMENT: BLACKBOARD QUIZ/WORKSHEET 2Review Assessment:Blackboard Quiz/Worksheet 2Matthew T Cook 1/19/10 11:45 PM Blackboard Quiz/Worksheet 2 Completed 105 out o
Oregon State - CHEM - 201
#include<stdio.h>/standardinputoutput #include<stdlib.h>/standardlibrarygcchello.cohello<enter>./hello #defineSIZE200 intlist[SIZE]; voidsort();intmain()cfw_ srand(time(NULL); inti; for(i=0i<15;i+)cfw_ list[i]=rand()%90+10; printf("HelloWorld!\n");retu
Oregon State - CHEM - 201
Lecture 2: Number SystemsSupplementary Notes Complements Floating-point NumbersCS1104-2aNumber Systems Supplementary Notes1Complements (1/4) Find the complement of a number is the short way ofsaying find the negated value in the complement system.
Oregon State - CHEM - 201
Homework 1Matthew Shuman Due October 5th, 20091Number System Conversions1. Convert (23)10 Binary 2. Convert (23)10 Hexidecimal 3. Convert (23)7 Base 6 4. Convert (23)16 Binary 5. Convert (23)8 Binary2Complements1. Find the 7 digit 1s complement of
Oregon State - CHEM - 201
Due: 10/12/2009ECE 271, Homework #2Instructor: Matt Shuman1) Simplify the following expressions using Boolean Algebra. a. Z = A + ( A*B ) b. Y = C * (C + 0) c. X = E + (D * D + E * 1) 2) List the truth table for the following Boolean Functions a. W = F
Oregon State - CHEM - 201
Matthew Cook ECE 272 Lab 3 Questions A) I was not involved in the ROV as a freshman. The only thing we did as a freshman was program a something on a micro chip. It was designed to turn lights on when certain buttons were pushed. This design was very comp
Oregon State - CHEM - 201
Lecture 2: Digital Systems and Binary NumbersMatthew Shuman October 2nd, 20091Complements 1-5 in TextThe meaning of complement is something required to make a thing complete. For example, salsa complements tortilla chips, beer complements pizza, an ic
Oregon State - CHEM - 201
Matthew Cook ENGR 272 Lab 4 4 A) Ok lets start with changing the program in which we design our digital logic Xilinx. That program was very difficult to deal with, and caused headache and grief within the team. I felt like the instructions were a little v
Oregon State - CHEM - 201
Matthew Cook ECE 272 Study QuestionStudyQuestion: If you implemented a Mealy model, comment on how the TekBot would react differently if you had implemented a Moore model. If you implemented a Moore model, comment on how the TekBot would react differentl
Oregon State - CHEM - 201
Matthew Cook ECE 272 A) Another interfacing problem could be hooking the wires up to incorrect pins. Or even putting the wires in too far, causing a fluctuating current. This in turn messes with your outputs. B) Now, you want a 5V output so we'll have tha
Oregon State - CHEM - 201
HHS 231 Text book and clicker Final Exam 7 30 am Monday March 15th Multiple choice, matching and True and False
Oregon State - CHEM - 201
Goal Order Circuit A1Freq (days) Exercise 23 SquatIntensity Sets 4070% 3 3 4070% 3 7076% 7883% 3 80%+ variesReps Rest 1215 10s 10s 1520 10s 912 58 90s 15 13SetsRest (Btwn sets)RepSpeed#Exercises (permajor muscle) 12 12 25 23 12 113circuitsLittleor
Oregon State - CHEM - 201
LIFETIME FITNESS FOR HEALTH (HHS_231_001_W2010) (HHS_231_001_W2010) > BB ASSIGNMENTS > REVIEW ASSESSMENT: BB ASSIGNMENT # 2 UPDATED FOR WINTER 2010Review Assessment: Bb Assignment # 2UPDATED FOR WINTER 2010Matthew T Cook 1/24/10 4:22 PM Bb Assignment #
Oregon State - CHEM - 201
MentalFlexibilityLectureOutlineWeek71. Benefits of Physical Flexibility List 3 Improved posture, more flexible, mental relaxation, reduced injury2. Flexibility is. Highly adaptable and increased by stretching. (range of motion in joint) Static stretchin
Oregon State - CHEM - 201
Based on the information you provided, this is your daily recommended amount from each food group.GRAINS8 ouncesMake half your grains wholeAim for at least 4 ounces of whole grains a dayVEGETABLES3 cupsVary your veggiesAim for these amounts each w
Oregon State - CHEM - 201
M atthew T. Cook Questions and Answers PHP Physical Analysis 1. After completing the 2 day activity assessment and fi tness testing exercises, w hat are 2 things you learned about your physical activity levels?T wo things that I learned about my physical
Oregon State - CHEM - 201
General Purpose: To inform Specific Purpose: At the end of the speech, the audience will know how to change oil in a car. Central idea: Oil Change: Whats liquidly, black, and needs to be changed about every 3,000 miles? Oil in the engine of a car. Today I
Oregon State - CHEM - 201
Cook 7 Work Cited Allen, Mike. Experts Rate Oil Change as Top Priority Oil IS Like Bodys Heart: Without Regular Checkups, It Can Kill Autos Engine Popular Mechanics. Dec 2003. Vol. 180, Iss. 12;pg. 124, 3 Oct. 2006 <http:/80proquest.umi.com.adam2.byui.ed
Oregon State - CHEM - 201
Cook 1 Matthew Cook Sister Pigott Eng. 111 5 October 2006 How to change your oil Imagine you are in a car and youre driving to your girlfriends house for dinner and a movie, and your engine all of a sudden heats up and he pulls to the side of the road. Th
Oregon State - CHEM - 201
General Purpose: Specific Purpose: At the end of the speech, the audience will know how to change oil in a car. Intro: Story regarding a bad incident where someone took there car in for a professional oil change: An oil change is only as professional as t
Oregon State - CHEM - 201
Work Cited Allen, Mike. Experts Rate Oil Change as Top Priority Oil Web. 02 Nov 2009. IS Like Bodys Heart: Without Regular Checkups, It Can Kill Autos Engine Popular Mechanics. Dec 2003. Vol. 180, Iss. 12; pg. 124, 3 Oct. 2006 <http:/80proquest.umi.com.ad
Oregon State - CHEM - 201
Matthew Cook Speech 111 Outline Due Wed Oct 7 3-5 Min Speech Intro: I. Introduce my self (Name). Something interesting about me is my heritage. Im half Canadian and half American. A. How my mom came to America. B. Born and raised in Hermiston Oregon. (des
Oregon State - CHEM - 201
Topic: FileSharingI.AttentionGetter:Isitlegaltoburnacdforyourfriend?Doyoudoit?II. PreviewoftheMainPoints:TodayIwilltalktoyouaboutwhatIusefilesharingfor, whatsbeingdonetodiscourageitsuse,andwhythoseeffortsindiscouragingitwill ultamatelyfail. III. MainPo
Oregon State - CS - 161
/* * Discription: Creates a full deck of cards shuffled and ready * to be dealt. */ import java.util.Arrays; import java.util.Collections; i import java.util.Random; public class CardDeck extends LinkedList cfw_ /52-card deck char[] number = cfw_'A','1','
Oregon State - CS - 161
/* * Discription: Creats a game of cards */ public class Game cfw_ String[] players = new String[] cfw_ "Dr. Zoiburg", "President Obama", "Daniel", "Cynthia" ; CardHand[] hands = new CardHand[4]; CardDeck deck; /* * Game() - constructor that runs the game
Oregon State - CS - 161
/* * Discription: A program that takes a deck of cards and deals them * to four players. Tis is done using a Linked List * and nodes. */ i import java.util.Scanner; public class TheMainClass cfw_ /* * main() - Driver method * Creates a game and loops till
Oregon State - CS - 161
http:/www.wikihow.com/Convert-from-Decimal-to-Binary
Oregon State - ECE - 271
Oregon State - CHEM - 201
Notes from Fundamentals of Software Engineering (Ghezzi et al. 1991)I. Types of Software Qualities External Qualities In general, these are qualities that the user sees and cares about.Ex. reliability and user friendliness Internal Qualities These are q
Oregon State - MATH - 254/255
Oregon State - MATH - 254/255
Oregon State - CHEM - 201
Homework 7Matthew Shuman Due November 13th, 20091State MachineDocument all 7 steps for a state machine necessary to drive a NES controller. Look at Lecture 13 for more details. 1. Dene the state machine requirements 2. State diagram 3. State assignmen
Oregon State - CHEM - 201
Chemistry 201 Final ExamFall 2009 December 9Oregon State University DrapelaDO NOT OPEN THIS EXAM UNTIL INSTRUCTEDInstructions: 1. Fill in the front page of the Scantron answer sheet with your last name, first name, and middle initial. Fill in the circ
Oregon State - CHEM - 201
CH 201 General Chemistry for Engineering MajorsDrapelaWelcome to ChemistryInstructor: Dr. Nicholas Drapela, Gilbert 231 Meeting times Tues,Thurs 80 minutesSections 8am 001 10am 003 Noon 002SyllabusThe complete syllabus is online at Blackboard; s
Oregon State - CHEM - 201
CH 201Tuesday, October 13 Ionic Formulas and NamesLast TimeTips for factor-label problems Convertingratios Units with exponents Atomic Structure Groups of elements Metals and nonmetals Formation of molecular compounds and ionic compoundsReview Que
Oregon State - CHEM - 201
CH 201Thursday, October 15 The MoleAnnouncement World premiere of Not Evil Just Wrong This Sunday, October 18 7pm, Milam Auditorium, OSU campus Free of charge Extra credit for CH 201 available Pickup question sheet if interestedMark your calendarR
Oregon State - CHEM - 201
CH 201 Chemistry For Engineering Majors Fall 2009Dr. Nick Drapela Office: 231 Gilbert Hall nick.drapela@orst.edu Office hours: W 10-11am W 2-3pmI. Required Course Materials- Masterton, Hurley Chemistry: Principles and Reactions, 6th Edition, Brooks/Col
Oregon State - CS - 161
INTRO TO COMPUTER SCIENCE I (CS_161_001_W2010) (CS_161_001_W2010) > ASSIGNMENTS > REVIEW ASSESSMENT: BLACKBOARD QUIZ/WORKSHEET 4Review Assessment: BlackboardQuiz/Worksheet 4Matthew T Cook 1/26/10 11:53 AM Blackboard Quiz/Worksheet 4 Completed 70 out of
Oregon State - CS - 161
Midterm 1 Study GuideLook over the Practice Exam at the top of our Announcement page for weeks 1-4. Read the Comments carefully so that you understand WHY. Look over your BBWS 1-4. Go to Blackboard -> Tools -> My Grades and click on a Blackboard quiz sco