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4. PARALLEL OPERATION
Parallel operation of transformers is effected when both the HV and LV windings of two (or more) transformers are connected to the same set of HV and LV busbars, respectively. Since connecting two impedances in parallel will result in a combined impedance which is very much less than either of the components (paralleling two identical transformers results in a combination which has an impedance of half that of each, individually), the primary result of this is to increase the fault level of the LV busbar. Care must therefore be taken to ensure that the fault capability of the LV switchgear is not exceeded. Unless fuse protection is provided each of the outgoing circuits would also need to be designed and cabled to withstand the full fault level of the paralleled transformers.
In the study of the parallel operation of transformers, polarity and phase sequence play important parts, and so it is essential to consider these characteristics in some detail before passing on to the more general treatment of parallel operation. The points to consider are the relative directions of the windings, the voltages in the windings and the relative positions of leads from coils to terminals. To understand how each of these factors interact it is best to consider transformer operation in instantaneous voltage terms relating directly to a phasor diagram, that is by studying transformer polarity diagrams basing an explanation upon the instantaneous voltages induced in both windings, as this procedure avoids any reference to primary and secondary windings. This can be seen to be logical as transformer polarity and phase sequence are independent of such a distinction.
As discussed in Section 2, the voltages induced in the primary and secondary windings are due to a common flux. The induced voltages in each turn of each of the windings must be in the same direction, since any individual turn can not be said to possess one particular direction around the core any more than it possesses the opposite one. Direction is given to a complete winding, however, when a number of these individual turns are connected in series, one end of the winding being labeled 'start' and the other 'finish,' or one being called, say, A1 and the other end A2. The directions of the total voltages induced in the primary and secondary windings will therefore depend upon the relative directions of the respective windings between their associated terminals. In considering direction of windings it is necessary to do so from similarly labeled or assumed similar terminals; that is, both primary and secondary windings should be considered in the direction from start to finish terminals (or even the reverse if desired), but they should not be considered one from start to finish and the other from finish to start. Where the start and finish of the windings are not known, adjacent primary and secondary terminals may be assumed initially to correspond to similar ends of the respective windings, but this must be verified by carrying out an induced voltage test at reduced voltage as described below.
Transformer terminal marking, position of terminals and phasor diagrams
Terminal markings
Transformer markings are standardized in various national specifications. For many years the British Standard, BS 171 (now superseded by EN 60076), has used ABCN, abcn as the phase symbols unlike many other parts of the world where the letters UVW, uvw have been used for the phases. A few years ago there was some move in the UK towards the adoption of the international UVW, uvw system. Further changes have been introduced by EN 60076-1: 1997 which uses Roman numerals I, II, III, and i, ii, iii. However, such changes must always be slow to take effect because of the amount of existing plant using the earlier systems. Some of the momentum for change now appears to have been lost so that all systems are in use in the UK. For this text the nomenclature ABCYN and abcyn is used since this is considered to be the clearest.
Individual-phase windings are given descriptive letters and the same letter in combination with suffix numbers is then used for all windings of one phase.
The HV winding has been given an upper case letter and the LV winding on the same phase a corresponding lower case letter. The following designations are used. For single-phase transformers:
A: for the HV winding 3A: for the third winding (if any) a: for the LV winding
For two-phase windings on a common core or separate cores in a common tank:
A B: for the HV windings a b: for the LV windings
For three-phase transformers:
A B C: for the HV windings 3A 3B 3C: for the third windings (if any) a b c: for the LV windings
FIG. 27 shows an example of standard marking of a single-phase transformer.
FIG. 27 Terminal marking of a single-phase transformer having a third
winding
Position of terminals
For three-phase transformers when facing the HV side the terminals are located from left to right NABC, and when facing the LV side cban. The neutral terminal may be at either end, but if no preference is stated, it should be at the left-hand end when viewed from the HV side and the LV neutral will accordingly be at the right-hand end when viewed from the LV side. Examples of both single- and three-phase terminal marking are shown in FIG. 28.
FIG. 28 Relative position of terminals of two-winding transformers.
In addition to the letter marking of terminals, suffix numbers are given to all tapping points and to the ends of the winding. These suffix numbers begin at unity and then with ascending numbers are ascribed to all tapping points, such that the sequence represents the direction of the induced e.m.f. at some instant of time. For three-phase star-connected windings lowest suffix numbered connections are taken to the neutral, highest numbered are taken to the line terminals. In the case of an HV winding without tappings for which the phase marking is A, the ends of the winding would be marked A1, A2. If this were the A phase of a three-phase star-connected transformer, A1 would be connected to the star point, A2 would be the line terminal. Similarly the LV winding would be marked a1, a2. As described later in this section, it is an easy matter to check the terminal marking (see FIG. 35). Typical examples of the marking of tappings are shown in FIG. 29.
The neutral connection, when brought out in the form of an external terminal, is marked YN in the case of an HV winding and yn in the case of an LV winding. No suffix number is required.
Autotransformer terminal marking includes the appropriate phase and suffix number and it should be noted that for tappings the higher suffix numbers correspond to the higher voltages. FIG. 29(d) shows a typical terminal marking for an autotransformer.
FIG. 29 Marking of tappings on phase windings.
Phasor diagrams
Phasors in transformer phasor diagrams represent the induced e.m.f.s and the counter-clockwise direction of rotation of the phasor is employed. The phasor representing any phase voltage of the LV winding is shown parallel to that rep resenting the corresponding phase voltage of the HV winding.
Various types of interphase connections for three-phase transformers having the same phase displacement between the HV and LV windings can be grouped together and the four groups are shown in Table 3.
Table 3 Group numbers
In Table 3 it will be seen that the phase displacement has a corresponding clock hour number. The phase displacement is the angle of phase advancement turned through by the phasor representing the induced e.m.f. between a HV terminal and the neutral point which may, in some cases, be imaginary, and the phasor representing the induced e.m.f. between the LV terminal having the same letter and the neutral point. An internationally adopted convention for indicating phase displacement is to use a figure which represents the hour indicated by a clock where the minute hand replaces the line to neutral voltage phasor for the HV winding and is set at 12 o'clock and where the hour hand represents the line to neutral voltage phasor for the LV winding. It there fore follows that the clock hour number is obtained by dividing the phase displacement angle in degrees by 30. The phase angles of the various windings of three-phase transformers are determined with reference to the highest voltage being taken as the phasor of origin.
The phasor diagram, the phase displacement and the terminal marking are all identifiable by the use of symbols which for transformers having two windings, if taken in order, have the following significance:
First symbol: HV winding connection.
Second symbol: LV winding connection.
Third symbol: phase displacement expressed as the clock hour number (see Table 3, column 3) The interphase connections of the HV and LV windings are indicated by the use of the initial letters as given in Table 4 and the terms high and low voltage used in this table are used in a relative sense only.
A transformer having a delta-connected HV winding, a star-connected LV winding and a phase displacement of plus 30º (corresponding to a clock hour number of 11), therefore has the symbol Dy11.
Table 4 Winding connection designations.
The following standard phasor diagrams which are frequently encountered in practice are included for single-, two- and three-phase transformers.
Three-phase transformers, phase displacement 0º see FIG. 30 Three-phase transformers, phase displacement 180º see FIG. 31 Three-phase transformers, phase displacement -30º see FIG. 32 Three-phase transformers, phase displacement _30º see FIG. 33 Single-, two-, three- to two-phase transformers see FIG. 34
Various other combinations of interphase connections having other phasor relationships occur but they are only infrequently manufactured and it is left to the reader to evolve the phasor diagram and symbol.
Polarity
In the more general sense the term polarity, when used with reference to the parallel operation of electrical machinery, is understood to refer to a certain relationship existing between two or more units, but the term can also be applied to two separate windings of any individual piece of apparatus. That is, while two separate transformers may, under certain conditions of internal and external connection, have the same or opposite polarity, the primary and secondary windings of any individual transformer may, under certain conditions of coil winding, internal connections, and connections to terminals, have the same or opposite polarity. In the case of the primary and secondary windings of an individual transformer when the respective induced terminal voltages are in the same direction, that is, when the polarity of the two windings is the same, this polarity is generally referred to as being subtractive; whilst when the induced terminal voltages are in the opposite direction, the windings are of opposite polarity, generally referred to as being additive.
FIG. 30 Phasor diagrams for three-phase transformers. Group number I:
phase displacement _ 0_
FIG. 31 Phasor diagrams for three-phase transformers. Group number II:
phase displacement _ 180 degrees.
This subject of polarity which was explained briefly in Section 2 can cause a great deal of confusion so it is worthwhile considering this a little more fully in order to obtain a complete understanding. It is helpful to consider, as an example, a plain helical winding, although, of course, the principle applies to any type of winding be this helical, disc or crossover coils.
FIG. 32 Phasor diagrams for three-phase transformers.
Group number III: phase displacement _ _30 degr.
FIG. 33 Phasor diagrams for three-phase transformers.
Group number IV: phase displacement _ _30 degr.
FIG. 34 Phasor diagrams for single-, two- and three- to two-phase transformers.
Starting from one end of a cylindrical former, assumed for the purpose of illustration to be horizontal, in order to produce a helical winding, it is most convenient for the winder to anchor the conductor to the top of the former and rotate this away from him, that is so that the upper surface moves away from him. If he starts at the left-hand end the conductor will then be laid in the manner of a normal right-hand screw thread and if he starts at the right hand end the conductor will take the form of a left-hand screw thread. If, at the completion of a layer, the winder wishes to continue with a second layer he must now start at the opposite end, so that if the first layer were wound left to right, the second layer will be wound right to left. The two layers thus wound will have additive polarity, that is, the voltage output from this two layer winding will be the sum of the voltages produced by each of the layers.
If, however, on completion of the first layer the winder had terminated the conductor and then started again winding a second layer from the same end as he started the first layer, and then connected together the two finishes, then the voltage output from this two-layer winding will be nil. These two layers have thus been wound with subtractive polarity. The foregoing description can be equally applicable to separate windings as to individual layers within a multilayer winding, so that the terms additive and subtractive polarity can be used to describe the manner of producing the windings of a complete transformer. The HV and LV windings of a two-winding transformer may thus have additive or subtractive polarity.
It will be seen from the above illustration that when both windings are wound in the same sense, the result is that their polarities are subtractive.
To determine the polarity of a transformer by testing, the method is to connect together corresponding terminals of HV and LV windings, FIG. 35, which is equivalent to the winder connecting together the corresponding ends of the layers of the two-layer windings in the above example. If the HV winding has terminals A1 and A2 and the LV winding a1 and a2, then if terminals A2 and a2 are connected together with a voltage applied to A1-A2, then the voltage measured across A1-a1 will be less than that applied to A1-A2 if the polarity is subtractive and more than that applied to A1-A2 if the polarity is additive.
Manufacturers will normally designate a particular method of winding, that is start left or start right as described in the above example, as their standard winding method. They will also have a standard method of designating terminals, say, 'starts' to become the lowest numbered terminal, 'finishes' to have the highest numbered terminal. They will then prefer to wind and connect the transformers according to these standards, in other words they will normally wind all windings in the same sense, so that most transformers will normally have subtractive polarity.
For three-phase transformers the testing procedure is similar, except that the windings must, of course, be excited from a three-phase supply, and consider ably more voltage measurements have to be made before the exact polarity and phase sequence can be determined. FIG. 36 shows the test connections and results for a star/star-connected transformer with subtractive polarity.
FIG. 36 Test connections for determining three-phase transformer winding
polarity
FIG. 35 Test connections for determining single-phase transformer
winding polarity
Phase sequence
Phase sequence is the term given to indicate the angular direction in which the voltage and current phasors of a polyphase system reach their respective maxi mum values during a sequence of time. This angular direction may be clock wise or counter-clockwise, but for two transformers to operate satisfactorily in parallel it must be the same for both. Phase sequence of polyphase transformers is, however, intimately bound up with the question of polarity.
It should be remembered that phase sequence is really a question of the sequence of line terminal voltages, and not necessarily of the voltages across individual windings. While the actual phase sequence of the supply is fixed by the system configuration and maintained by the generating plant, the sequence in which the secondary voltages of a transformer attain their maximum values can be in one direction or the other, according to the order in which the primary terminals of the transformer are supplied.
FIG. 37 Diagrams showing four examples of a three-phase delta/star-connected
transformer having differing polarity and phase sequence
FIG. 37 shows four instances of a delta/star-connected transformer under different conditions of polarity and phase sequence, and a comparison of these diagrams shows that interchanging any one pair of the supply connections to the primary terminals reverses the phase sequence. If, however, the internal connections on the secondary side of the transformer are reversed, the interchanging of any two primary supply connections will produce reverse phase sequence and non-standard polarity. If with reverse internal connections on one side the primary connections are not interchanged, the resulting phase sequence will be the same and the polarity will be non-standard. The above remarks apply strictly to transformers in which the primary and secondary windings have different connections, such as delta/star, but where these are the same, such as star/star, the polarity can only be changed by reversing the internal connections on one side of the transformer. The phase sequence alone may, however, be reversed by interchanging two of the primary supply leads.
If tests indicate that two transformers have the same polarity and reverse phase sequence, they may be connected in parallel on the secondary side simply by interchanging a certain pair of leads to the busbars of one of the transformers. Referring to FIG. 37, for instance, transformers to diagrams (a) and (d) can be paralleled so long as the secondary leads from a1 and c1 to the busbars are interchanged.
The satisfactory parallel operation of transformers is dependent upon five principal characteristics; that is, any two or more transformers which it is desired to operate in parallel should possess:
(1) The same inherent phase angle difference between primary and secondary terminals.
(2) The same voltage ratio.
(3) The same percentage impedance.
(4) The same polarity.
(5) The same phase sequence.
To a much smaller extent parallel operation is affected by the relative outputs of the transformers, but actually this aspect is reflected into the third characteristic since, if the disparity in outputs of any two transformers exceeds three to one it may be difficult to incorporate sufficient impedance in the smaller transformer to produce the correct loading conditions for each individual unit.
Characteristics 1 and 5 only apply to polyphase transformers. A very small degree of latitude may be allowed with regard to the second characteristic mentioned above, while a somewhat greater tolerance may be allowed with the third, but the polarity and phase sequence, where applicable, of all transformers operating in parallel must be the same.
Single-phase transformers
The theory of the parallel operation of single-phase transformers is essentially the same as for three phase, but the actual practice for obtaining suitable connections between any two single-phase transformers is considerably simpler than the determination of the correct connections for any two three-phase transformers.
Phase angle difference between primary and secondary terminals
In single-phase transformers this point does not arise, as by the proper selection of external leads any two single-phase transformers can be connected so that the phase angle difference between primary and secondary terminals is the same for each. Consequently, the question really becomes one of polarity.
Voltage ratio
It is very desirable that the voltage ratios of any two or more transformers operating in parallel should be the same, for if there is any difference whatever a circulating current will flow in the secondary windings of the transformers when they are connected in parallel, and even before they are connected to any external load. Such a circulating current may or may not be permissible. This is dependent firstly on its actual magnitude and, secondly, on whether the load to be supplied is less than or equal to the sum of the rated outputs of the transformers operating in parallel. As a rule, however, every effort should be made to obtain identical ratios, and particular attention should be given to obtaining these at all ratios when transformers are fitted with tappings. In passing, it may be well to point out that when a manufacturer is asked to design a transformer to operate in parallel with existing transformers, the actual ratio of primary and secondary turns should be given, as this ratio can easily be obtained exactly.
Such figures would, of course, be obtained from the works test certificate for the existing transformers.
Equations (Eqn. 8)-(Eqn. 26) inclusive show how the values of these circulating currents can be calculated when certain of the transformer characteristics differ. Equations (Eqn. 8)-(Eqn. 12) show how to derive the circulating currents when two single- or three-phase transformers, having different ratios, operate in parallel, while Eqs (Eqn. 13)-(Eqn. 17) apply to the case of three single- or three-phase transformers.
It is to be noted that this flow of circulating current takes place before the transformers are connected up to any external load. A circulating current in the transformer windings of the order of, say, 5 percent of the full-load cur rent may generally be allowed in the case of modern transformers without any fear of serious overheating occurring. It is sometimes very difficult to design new transformers to give a turns ratio on, say, four tappings identical to what an existing one may possess, and while it is desirable that the ratios should be the same, it is not necessary to insist on their being identical.
Equation (Eqn. 8): The circulating current in amperes at no-load in two single- or three-phase transformers A and B connected in parallel, having different voltage ratios, the same or different outputs, the same or different impedances, and the impedances having the same ratios of resistance to reactance, is equal to
(Eqn. 8)
where VA is the secondary line terminal voltage of transformer A having the lower ratio, that is the higher secondary voltage
VB is the secondary line terminal voltage for transformer B having the higher ratio, that is the lower secondary voltage
*ZA, ZB is the ohmic impedances of transformers A and B, respectively, and are obtained from the equations:
(Eqn. 9) where VZA, VZB is the percentage impedance voltage drops at full-load ratings of the transformers A and B, respectively
IA, IB is the full-load line currents in amperes of transformers A and B, respectively.
In the case of certain system transformers operating in parallel it is relatively common practice to set the on-load tapchangers to give a 'tap stagger' so that the system voltage profile at the point where the transformers are located can be varied by adjusting the reactive load flows at that point. Such practice results in local circulating currents between the transformers irrespective of their load throughput.
Equation (Eqn. 10): The circulating current in amperes at no load in two single- or three-phase transformers A and B connected in parallel, having different voltage ratios, the same or different outputs, the same or different impedances, but the impedances having different ratios of resistance to reactance, is equal to
(Eqn. 10) where VA is the secondary terminal voltage of transformer A, having the lower ratio, that is the higher secondary voltage
VB is the secondary line terminal voltage of transformer B, having the higher ratio, that is the lower secondary voltage
*Z is the vector sum of the ohmic impedances of transformers A and B, and is obtained from the equation
(Eqn. 11)
*These quantities are the transformer resistances and reactances between two secondary line terminals.
(Eqn. 12)
VRA, VRB are the percentage resistance voltage drops at normal full-load ratings of transformers A and B, respectively VXA, VXB are the percentage reactance voltage drops at normal full-load ratings of transformers A and B, respectively IA, IB are the normal full-load line currents in amperes of transformers A and B, respectively Equations (Eqn. 13)-(Eqn. 15): The circulating currents in amperes at no load in three single- or three-phase transformers A, B and C connected in parallel, each having different voltage ratios, the same or different impedances, the same or different outputs, and the impedances having the same ratio of resistance to reactance, are given by:
In transformer A
(Eqn. 13)
(Eqn. 14)
(Eqn. 15)
where VA is the secondary line terminal voltage of transformer A, having the lowest ratio, that is the highest secondary voltage
VB is the secondary line terminal voltage of transformer B, having the next higher ratio, that is the next lower secondary voltage
VC is the secondary line terminal voltage of transformer C, having the highest ratio, that is the lowest secondary voltage And where for transformers A, B and C, respectively, *ZA, ZB, ZC are the ohmic impedances and are obtained from the equations:
(Eqn. 16)
where VZA, VZB, VZC are the percentage impedance voltage drops at full-load ratings
IA, IB, IC are the full-load line currents in amperes
(Eqn. 17)
Equations (Eqn. 18)-(Eqn. 20): The circulating currents in amperes at no load in three single- or three-phase transformers A, B and C connected in parallel, having different voltage ratios, the same or different outputs, the same or different impedances, but the impedances having different ratios of resistance to reactance, are given by:
In transformer A In transformer B and in transformer C
(Eqn. 18)
(Eqn. 19)
(Eqn. 20)
(Eqn. 21)
(Eqn. 22)
The symbol 'S' has the usual mathematical significance, that is:
(Eqn. 23)
The angle of lag2
between the circulating current and the normal secondary line terminal voltages of transformers A, B and C, respectively is equal to:
(Eqn. 24)
(Eqn. 25)
(Eqn. 26)
where T and S have the same values as before. The remaining symbols used have the following meanings for transformers A, B and C, respectively,
VA, VB, VC are the secondary line terminal voltages
IA, IB, IC are the normal full-load line currents
VZA, VZB, VZC are the percentage impedance voltage drops at full-load rating
VRA, VRB, VRC are the percentage resistance voltage drops at full-load rating
VXA, VXB, VXC are the percentage reactance voltage drops at full-load rating.
[2 The angle of lag is taken as being positive. If the sign of any of these expression is negative the angle is leading.]
Percentage impedance voltage drop
The percentage impedance voltage drop is a factor inherent in the design of any transformer, and is a characteristic to which particular attention must be paid when designing for parallel operation. The percentage impedance drop is determined by the formula:
(Eqn. 27)
where VZ is the percentage impedance drop, VR is the percentage resistance drop and VX is the percentage reactance drop, corresponding to the full-load rating of the transformer. Assuming that all other characteristics are the same, the percentage impedance drop determines the load carried by each transformer, and in the simplest case, viz, of two transformers of the same output operating in parallel, the percentage impedances must also be identical if the transformers are to share the total load equally. If, for instance, of two transformers connected in parallel having the same output, voltage ratio, etc., one has an impedance of 4 percent and the other an impedance of 2 percent, the transformer having the larger impedance will supply a third of the total bank output and the other transformer will supply two-thirds, so that the transformer having the higher impedance will only be carrying 66 percent of its normal load while the other transformer will be carrying 33 percent overload.
Equations (Eqn. 28)-(Eqn. 48) inclusive show how the division of load cur rents can be calculated when certain of the transformer characteristics differ.
Equations (Eqn. 28)-(Eqn. 36) show how to derive the transformer load currents when two single- or three-phase transformers having different impedances operate in parallel, while Eqs (Eqn. 37)-(Eqn. 48) apply to the case of three single- or three-phase transformers.
When there is a phase displacement between transformer and total load cur rents, the phase angles can also be calculated from the equations.
Equations (Eqn. 28) and (Eqn. 29): The division of total load current IL amperes between two single- or three-phase transformers A and B connected in parallel, having the same or different outputs, the same voltage ratios, the same or different impedances, and the same ratios of resistance to reactance, is given by:
(Eqn. 28)
(Eqn. 29)
where, for transformers A and B, respectively, IA, IB is the line currents in amperes.
(Eqn. 30)
and KA, KB are the normal rated outputs in kVA
VZA, VZB are the percentage impedance voltage drops at full-load ratings Note: The load currents in transformers A and B are in phase with each other and with the total load current.
Equations (Eqn. 31) and (Eqn. 32): The division of total load current IL amperes between two single- or three-phase transformers A and B connected in parallel, having the same or different outputs, the same voltage ratios, the same or different impedances, but different ratios of resistance to reactance, is given by:
(Eqn. 31)
(Eqn. 32)
(Eqn. 33)
(Eqn. 34)
(Eqn. 35)
(Eqn. 36)
and where for transformers A and B, respectively, IA, IB are the line currents in amperes KA, KB are the normal rated outputs in kVA VZA, VZB are the percentage impedance voltage drops at full-load ratings
VXA, VXB are the percentage reactance voltage drops at full-load ratings VRA, VRB are the percentage resistance voltage drops at full-load ratings
? is the phase angle difference between the load currents IA and IB (see FIG. 38)
ß is the phase angle difference between IL and IB (see FIG. 38) a is the phase angle difference between IL and IA (see FIG. 38)
FIG. 38 Phasor diagram showing current distribution with three transformers in parallel having different ratios of resistance to reactance
For the diagram in FIG. 38:
? is positive.
IA is leading IL.
IB is lagging IL.
Transformer A has the smaller value of VX/VR.
Transformer B has the greater value of VX/VR.
When ? is negative:
IA is lagging IL.
IB is leading IL.
Transformer A has the greater value of VX/VR.
Transformer B has the smaller value of VX/VR.
Equations (Eqn. 37)-(Eqn. 39): The division of total load current IL between three single- or three-phase transformers A, B and C connected in parallel, having the same or different outputs, the same voltage ratio, the same or different impedances, and the same ratios of resistance to reactance, is given by:
(Eqn. 37)
(Eqn. 38)
(Eqn. 39)
(Eqn. 40)
and where KA, KB, KC are the normal rated outputs in kVA
VZA,VZB,VZC are the percentage impedance voltage drops at full-load ratings Equations (Eqn. 41)-(Eqn. 43): The division of total load current IL between three single- or three-phase transformers A, B and C connected in parallel, having the same or different outputs, the same voltage ratios, the same or different impedances, but different ratios of resistance to reactance, is given by:
(Eqn. 41)
(Eqn. 42)
(Eqn. 43)
where IA, IB, IC are the line currents in amperes
k1 is a constant and equals:
(Eqn. 44)
(Eqn. 45)
(Eqn. 46)
(Eqn. 47)
(Eqn. 48)
FIG. 39 Phasor diagram showing current distribution with three transformers
in parallel having different ratios of resistance to reactance.
and where for transformers A, B and C, respectively, KA, KB, KC are the normal rated outputs in kVA VZA, VZB, VZC are the percentage impedance voltage drops at full-load ratings VXA, VXB, VXC are the percentage reactance voltage drops at full-load ratings VRA, VRB, VRC are the percentage resistance voltage drops at full-load ratings
?1 is the phase angle difference between the load currents IA and IB
?2 is the phase angle difference between the load currents IB and IC From the geometry of the figure:
and the phase angle difference between the load current IA in transformer A and the total load current IL is (?1 - ß _ a). Having fixed the phase relation ship of the total load current to the load current in one transformer, it is a simple matter to determine the angles between the total load current and the load currents in the remaining two transformers. If ß is greater than a, the load cur rent IB in transformer B is lagging with respect to IL: if ß is smaller than a, IB is leading with respect to IL.
For the diagram in FIG. 39:
?1 and ?2 are positive.
IA is leading IL.
IC is lagging IL.
Transformer A has the smallest ratio of VX/VR.
Transformer C has the greatest ratio of VX/VR.
IB may lead or lag IL, according to the interrelationship of its value of VX/VR with the values of VX/VR of the other two transformers.
When ?1 and ?2 are negative:
IA is lagging IL.
IC is leading IL.
Transformer A has the greatest ratio of VX/VR.
Transformer C has the smallest ratio of VX/VR.
As before, IB may lead or lag IL, depending upon the various values of VX/VR.
When dealing with transformers having different outputs and different impedances which are to operate in parallel, it should be remembered that the impedance drop of a single transformer is based on its own rated full-load cur rent, and this point should not be overlooked when determining the current distribution of two such transformers operating in parallel. If the ohmic values of the impedances of the individual transformers are deduced from the impedance drop and normal full-load current of each and the results inserted in the usual formula for resistances in parallel, the same final results for current distribution are obtained by already well-known and simple methods. In using this ohmic method care should be taken to notice whether the ratio of resistance to reactance is the same with all transformers, for, if it is not, the value of the impedance voltage drop as such cannot directly be used for determining the current distribution, but it must be split up into its power and reactive components.
When operating transformers in parallel the output of the smallest transformer should not be less than one-third of the output of the largest, as other wise it is extremely difficult, as mentioned above, to incorporate the necessary impedance in the smallest transformer.
Polarity
The term polarity when used with reference to the parallel operation of electrical machinery is generally understood to refer to a certain relationship existing between two or more units, though, as stated previously, it can be applied so as to indicate the directional relationship of primary and secondary terminal voltages of a single unit. Any two single-phase transformers have the same polarity when their instantaneous terminal voltages are in phase. With this condition a voltmeter connected across similar terminals will indicate zero.
Single-phase transformers are essentially simple to phase in, as for any given pair of transformers there are only two possible sets of external connections, one of which must be correct. If two single-phase transformers, say X and Y, have to be phased in for parallel operation, the first procedure is to connect both primary and secondary terminals of, say, transformer X, to their corresponding busbars, and then to connect the primary terminals of transformer Y to their busbars. If the two transformers have the same polarity, corresponding secondary terminals will be at the same potential, but in order to ascertain if this is so it is necessary to connect one secondary terminal of transformer Y to what is thought to be its corresponding busbar. It is necessary to make the connection from one secondary terminal of transformer Y, so that when taking voltage readings there is a return path for the current flowing through the volt meter. The voltage across the disconnected secondary terminal of transformer Y and the other busbar is then measured, and if a zero reading is obtained the transformers have the same polarity, and permanent connections can accordingly be made. If, however, the voltage measured is twice the normal secondary voltage, then the two transformers have opposite polarity. To rectify this it is only necessary to cross-connect the secondary terminals of transformer Y to the busbars. If, however, it is more convenient to cross-connect the primary terminals, such a procedure will give exactly the same results.
Phase sequence
In single-phase transformers this point does not arise, as phase sequence is a characteristic of polyphase transformers.
Polyphase transformers
Phase angle difference between primary and secondary terminals The determination of suitable external connections which will enable two or more polyphase transformers to operate satisfactorily in parallel is more complicated than is a similar determination for single-phase transformers, largely on account of the phase angle difference between primary and secondary terminals of the various connections. It becomes necessary, therefore, to study carefully the internal connections of polyphase transformers which are to be operated in parallel before attempting to phase them in.
Transformers made to comply with the same specification and having similar characteristics and phase-angle relations can be operated in parallel by connecting together terminals with the same symbol. With reference to Figs 30-33 transformers belonging to the same group number may be operated in parallel; in addition it is possible to arrange the external connections of a transformer from group number 3 to enable it to operate in parallel with another transformer connected to group number 4 without changing any internal connections. FIG. 40 indicates how this can be achieved, and it will be seen that two of the HV connections and the corresponding LV connections are interchanged.
FIG. 40 Example of parallel operation of transformers in groups 3 and
4. The phasor diagram of the transformer Dy1 is identical with FIG. 32, but
that for the transformers Yd11, for which the phase sequence has been reversed
from A-B-C to A-C-B, differs from FIG. 33.
FIG. 41 Diagram showing the pairs of three-to three-phase transformer
connections which will and which will not operate together in parallel.
Transformers connected in accordance with phasor groups 1 and 2, respectively cannot be operated in parallel with one another without altering the internal connections of one of them and thus bringing the transformer so altered within the other group of connections.
FIG. 41 shows the range of three-to three-phase connections met with in practice, and it will be noticed that the diagram is divided up into four main sections. The pairs of connections in the groups of the upper left-hand section may be connected in parallel with each other, and those in the lower right-hand section may also be connected in parallel with one another, but the remaining pairs in the other two groups cannot so be connected, as there is a 30º phase displacement between corresponding secondary terminals. This displacement is indicated by the dotted lines joining the pairs of secondaries.
It should be noted that this question of phase displacement is one of displacement between the line terminals, and not necessarily of any internal displacement which may occur between the phasors representing the voltages across the individual phase windings.
Voltage ratio
With polyphase transformers, exactly the same remarks apply as outlined for single-phase transformers. Equations (8)-(26), inclusive, also apply in the same way, but the currents, voltages and impedances should all be based on the line values.
Percentage impedance
The treatment given in Eqs (28)-(48), inclusive, applies exactly for poly phase transformers, the currents, voltages and impedances being based on-line values.
Polarity and phase sequence
When phasing in any two or more transformers it is essential that both their polarity and phase sequence should be the same. The phase sequence may be clockwise or counterclockwise, but so long as it is the same with both transformers, the direction is immaterial. It is generally advisable, when installing two or more transformers for parallel operation, to test that corresponding secondary terminals have the same instantaneous voltage, both in magnitude and phase.
With regard to the actual procedure to be followed for determining the correct external connections, there are two ways in which this may be done.
The first one is to place the two transformers in parallel on the primary side and take voltage measurements across the secondaries, while the other is to refer to the manufacturer's diagram. FIG. 42 shows examples of two typical nameplate diagrams, that in FIG. 42(a) is for a transformer having fairly simple connections and off-circuit tappings, while that in FIG. 42(b) shows a more complex arrangement having tappings selected on load by means of a 19 position tapchanger and an arrangement of links which allows alternative connections for YNd1 and YNd11 winding arrangements to be obtained. From a diagram of this kind, together, if necessary, with the key diagrams which are given in FIG. 43, it is an easy matter to obtain precisely the correct external connections which will enable the transformers to operate in parallel.
FIG. 42(a) Manufacturer's nameplate diagram of connections
FIG. 42(b) Manufacturer's nameplate diagram of connections
FIG. 43 Key diagrams for the phasing-in of three-to three-phase transformers.
FIG. 44 Phasing-in a three-phase transformer.
Dealing first with the method in which a series of voltage readings are taken for the purpose of determining how the transformers shall be connected, assume two transformers X and Y having the same voltage ratios and impedances and with their internal connections corresponding to any one pair of the permissible combinations given in FIG. 41. The first procedure is to connect all the primary terminals of both transformers to their corresponding busbars, and to connect all the secondary terminals of one transformer, say X, to its busbars. Assuming that both secondary windings are ungrounded, it is next necessary to establish a link between the secondary windings of the two transformers, and for this purpose any one terminal of transformer Y should be connected, via the busbars, to what is thought to be the corresponding terminal of the other transformer. These connections are shown in FIG. 44. Voltage measurements should now be taken across the terminals aa_ and bb_, and if in both instances zero readings are indicated, the transformers are of the same polarity and phase sequence, and permanent connections may be made to the busbars. If, however, such measurements do not give zero indications, it is sometimes helpful to take, in addition, further measurements, that is, between terminals ab_ and ba_, as such measurements will facilitate the laying out of the exact phasor relationship of the voltages across the two transformer secondary windings FIG. 43 gives key diagrams of the different positions that the secondary voltage phasors of a transformer could take with respect to another transformer depending upon their relative connections, polarity, phase sequence and the similarity or not of those terminals which form the common junction, and this will serve as a guide for determining to what the test conditions correspond on any two transformers.
In the case of transformers of which the primary and secondary connections are different, such as delta/star, it is only necessary when one of the transformers is of opposite polarity, to change over any two of the primary or secondary connections of either transformer. As such a procedure also reverses the phase sequence, care must be exercised finally to join those pairs of secondary terminals across which zero readings are obtained. When, however, the connections on the primary and secondary sides are the same, such as, for instance, delta/ delta, transformers of opposite polarity cannot be phased in unless their internal connections are reversed. When the phase sequence is opposite, it is only a question of changing over the lettering of the terminals of one transformer, and, provided the polarity is correct, connecting together similarly lettered terminals; in other words, two of the secondary connections of one transformer to the busbars must be interchanged. With two transformers both having star connected secondaries, the preliminary common link between the two can be made by connecting the star points together if these are available for the purpose, and this leaves all terminals free for the purpose of making voltage measurements. As a result, this procedure makes the result much more apparent at first glance owing to the increased number of voltage measurements obtained.
Dealing next with the method in which the transformer manufacturer's diagram is used for obtaining the correct external connections, FIG. 45 shows the six most common combinations of connections for three- to three-phase transformers. This diagram illustrates the standard internal connections between phases of the transformers, and also gives the corresponding polarity phasor diagrams. It is to be noted that the phasors indicate instantaneous induced volt ages, as by arranging them in this way the phasor diagrams apply equally well irrespective of which winding is the primary and which the secondary.
Both primary and secondary coils of the transformers are wound in the same direction, and the diagrams apply equally well irrespective of what the actual direction is. With the standard polarities shown in FIG. 45, it is only necessary to join together similarly placed terminals of those transformers which have connections allowing of parallel operation, to ensure a choice of the correct external connections. That is, there are two main groups only, the first comprising the star/star and the delta/delta connection, while the other consists of the star/delta, delta/star, interconnected star/star and star/interconnected star.
When phasing in any two transformers having connections different from the star or the delta, such as, for instance, two Scott-connected transformer groups to give a three- to two-phase transformation, particular care must be taken to connect the three-phase windings symmetrically to corresponding busbars. If this is not done the two-phase windings will be 30º out of phase, and FIG. 46 shows the correct and incorrect connections together with the corresponding phasor diagrams.
FIG. 45 Standard connections and polarities for three-to three phase transformers.
Note: primary and secondary coils wound in the same direction;
• indicates start of windings, _ indicates finish of windings
FIG. 46 Correct and incorrect method of paralleling two Scott-connected
groups for three- to two-phase transformation.
A further point to bear in mind when phasing in Scott-connected transformer banks for two- to three-phase transformation is that similar ends of the teaser windings on the primary and secondary sides must be connected together. This applies with particular force when the three-phase neutrals are to be connected together for grounding. If the connection between the teaser transformer and the main transformer of one bank is taken from the wrong end of the teaser winding, the neutral point on the three-phase side of that bank will be at a potential above ground equal to half the phase voltage to neutral when the voltage distribution of the three-phase line terminals is symmetrical with respect to ground.
Other features which should be taken into account when paralleling transformers may briefly be referred to as follows:
(1) The length of cables on either side of the main junction should be chosen, as far as possible, so that their percentage resistance and reactance will assist the transformers to share the load according to the rated capacity of the individual units.
(2) When two or more transformers both having a number of voltage adjusting tappings are connected in parallel, care should be taken to see that the transformers are working on the same percentage tappings. If they are connected on different tappings, the result will be that the two transformers will have different ratios, and consequently a circulating current will be produced between the transformers on no-load.
The parallel operation of networks supplied through transformers
Thus far this section has dealt exclusively with the parallel operation of transformers located in the same substation or supplying a common circuit. As the loads on a given system increase and as the system extends, due to new load requirements in more distant areas of supply, it frequently becomes necessary to interconnect either, or both, the HV and LV networks at different points, in order to produce an economical distribution of load through the mains, and to minimize voltage drops at the more remote points of the networks. This problem of network interconnection due to increasing loads and extended areas of supply becomes, perhaps, most pressing in the case of systems which originally have been planned, either partially or wholly, as radial systems.
In such cases, particularly, perhaps, when the problem is one of interconnecting higher-voltage supplies to extensive LV networks, it may be found that the different circuits between the common source of supply and the proposed point, or points, of interconnection, contain one or more transformers, which may, or may not, have the same combinations of primary and secondary connections, the same impedances, etc. The different circuits, moreover, may not contain the same number of transforming points.
It has been stated previously that two delta/star or star/delta transformers, for instance, may be paralleled satisfactorily simply by a suitable choice of external connections to the busbars, provided their no-load voltage ratios are the same, and such transformers will share the total load in direct proportion to their rated outputs provided their percentage impedances are equal. When, however, two or more compound circuits each comprising, say, transformers and overhead lines, or underground cables, are required to be connected in parallel at some point remote from the source of supply, the question of permissible parallel operation is affected by the combined effect of the numbers of transformers in the different circuits and the transformer connections.
A typical instance of what might be encountered is shown in FIG. 47 where a common LV network is fed from a power station through two parallel HV circuits A and B, one of which, A, contains a step-up transformer and a step-down transformer, both having delta-connected primaries and star connected secondaries, while the other, B, contains one transformer only, having its primary windings delta connected and its secondary windings in star. From such a scheme it might be thought at first that the switches at the points X and Y might be closed safely, and that successful parallel operation would ensue.
Actually, this would not be the case.
FIG. 47 Network layout
FIG. 48 shows the phasor diagrams of the voltages at the generating station and at the different transforming points for the two parallel circuits lying between the power station and the common LV network, and it will be seen from these that there is a 30º phase displacement between the secondary line of neutral voltage phasors of the two transformers, (2) and (3), which are connected directly to the LV network. This phase displacement cannot be eliminated by any alternative choice of external connections to the busbars on either primary or secondary sides of any of the delta/star transformers, nor by changing any of the internal connections between the phase windings. The difficulty is created by the double transformation in circuit A employing delta/star connections in both cases, and actually the sum total result is the same as if the two transformers concerned were connected star/star. As mentioned earlier in this section, it is impossible to connect a star/star transformer and a delta/star in parallel.
FIG. 48 Connections not permitting parallel operation.
FIG. 49 Connections permitting parallel operation.
The two circuits could be paralleled if the windings of any of the three transformers were connected star/star as shown in FIG. 49(a-c) or delta/inter connected star as shown in of FIG. 50(a-c).
Apart from the fact that the delta/interconnected star transformer would be slightly more expensive than the star/star, the advantage lies with the former, as it retains all the operating advantages associated with a primary delta winding.
FIG. 50 Alternative connections permitting parallel operation.
The phasor diagram in FIG. 51 shows the relative voltage differences which would be measured between the secondary terminals of the two transformers, (2) and (3), assuming their neutral points were temporarily connected together for the purpose of taking voltmeter readings, and that all three transformers were delta/star connected as in FIG. 48.
FIG. 51 Phasor diagram of LV voltages corresponding to FIG. 48
With properly chosen connections, as shown in Figs 49 and 50, the loads carried by the two parallel circuits A and B will, of course, be in inverse pro portion to their respective sum total ohmic impedances.
Thus, when laying out a network supplied through the intermediary of transformers, the primary and secondary connections of the latter, at the different transforming centers, should be chosen with a view to subsequent possible network interconnections, as well as from the other more usual considerations governing this question.