US2264836A - Electric distribution system and multiwinding transformer therefor - Google Patents

Description

1941- 4 A. N. GARIN 2,264,836

ELECTRIC DISTRIBUTION SYSTEM AND MULTIWINDING TRANSFORMER THEREFOR .-.Filed March 14, 1940 2 Sheets-Sheet 1 Inventor I Alexis N. Gavin,

His ttorneg.

D66. 2, A. N. GARIN ELECTRIC DISTRIBUTION SYSTEM AND MULTIWINDING TRANSFORMER THEREFOR Filed March 14, 1940 2 Shets-Sheet 2 Fig.6. 4 g

lnvenbori Alexis N. Gavin,

His Attorney rulcntcu "CC. 1, lU'Ol UNITED STATES amoqpoo PATENT OFFICE ELECTRIC ITISTRIBUTION SYSTEM AND MULTIWINDING TRANSFORMER THERE- FOB Alexis N. Garin, Pittsfield, Mass assignor to General Electric Company, a corporation of New York 18 Claims.

My invention relates to alternating current distribution systems and more particularly to multiwinding transformers having four or more windings and their arrangements and connections in such systems. v

An object of my invention is to provide new and improved arrangements for multiwinding transforming apparatus in systems of distribution for improving the operation of such systems.

It is another object of my invention to obtain in a system of distribution having connected therein a multiwinding transforming means of four or more windings a predetermined most ad,- vantageous distribution of load and also to obtain a predetermined most advantageous relationship of terminal voltages of said transforming means under various loading conditions.

It is another object of my invention to provide a new and improved multiwinding transformer having four or more windings.

It is another object of my invention to provide" a multiwinding transformer of four or more windings having such characteristics as to secure a predetermined interaction between pairs of windings under load whereby a desired division of current or load between a given pair of windings may be secured for a given relative loading of another pair of windings.

It is another object of my invention to provide a multiwinding transformer of four or more windings having such characteristics as to secure a predetermined relation between terminal voltages of a given pair of windings independently of the relative loading of another pair of windings.

My invention will be better understood from the following description taken in connection with the accompanying drawings, and its scope will be pointed out in the appended claims.

While the use of multiwinding transformers having four or more windings for purposes such as that of supplying a plurality of loads of different voltages is not new, their use for improving system operation by providing, for instance, duplicate windings having the same voltage rating and connected to different parts of the system respectively, is relatively recent and has presented to the art a number of new problems not encountered in the use of two-winding or threewinding transformers and not encountered in the use of n-winding transformers supplying for instance n-l independent loads from a common source.

Whenever a pair of the windings of a multiwinding transformer of four or more windings is connected into a loop, or to two separate sources of power, respectively, or in any other arrangement permissive of exchange of power or circulation of power between that pair of windings, the division of load within that pair of windings, and the relationship of other electrical characteristics of that pair of windings, may be greatly influenced by the condition of relative loading of the other windings of the transformer. As the most favorable value of such an effect depends on the needs and requirements of the particular system to which the multiwinding transformer is to be connected, the present invention is directed to the construction and circuit connections of a multiwinding transformer of four or more windings for securing inherently a predetermined most advantageous distribution of load in such.

systems and for securing inherently a predetermined most advantageousrelationship of terminal voltages under various loading conditions.

In the drawing, Fig. 1 is a conventional schematic single-wire diagram of a four-winding transformer in a very simple system connection involving a loop for the exposition of the physical conceptions and mathematical principles underlying the invention; Fig. 2 is a modification of Fig. 1 to illustrate the effect of impedances external to the transformer windings in such loops; Fig. 3 is a modification of Fig. 2 with the introduction into the loop of a variable voltage external to the transformer and intended to modify the load division between the branches of the loop and their corresponding transformer windings; Fig. 4 illustrates an embodiment in which a pair of the windings of a multiwinding transformer are connected respectively to a pair of independently controlled generators; Fig. 5 illustrates schematically the connections of a sixwinding transformer in a system involving two pairs of the windings in loops; Fig. 6 is a diagrammatic illustration of a single-phase multiwinding transformer comprising three pairs of windings so arranged as to make the division of load and terminal voltage balance within each pair independent of the relative loading of any other pair; and Fig. 7 is a schematic equivalent network of the transformer of Fig. 6. Like reference characters indicate similar parts in the several figures of the drawings.

Referring now to Fig. l of the drawings, a schematic single-wire diagram is shown as illustrative of a four-winding single-phase transformer and system of connections in accordance with my invention, having a pair of primary windings l and 2 and a pair of secondary windings 3 and 4. Primary winding I is supplied from a source of alternating current 'I through a bus 8 and circuit interrupting device 9. Primary winding 2 may, for example, be of the same voltage rating as primary winding I and is similarly supplied from the same source I and bus 8 but through an independent connection to the bus through circuit interrupting device I0. It is seen that windings I and 2 are connected in parallel. Secondary winding 3 is connected to a load II and secondary winding 4 to another independent load, I2. As'loads II and I2 are independent, the voltampere power delivered by winding 3 to load II may have any ratio to that delivered by winding 4 to load I 2.

The mathematic theory on which the invention is based will now be considered. Let the load current in each winding be designated by I with appropriate subscripts corresponding to the number of the winding, as 11,12, I: and I4, respectively.

In the following exposition and equations, these currents may be understood as expressed either in amperes, or ampere-turns, or per unit values, equally well; all three systems of units being wellknown in the art. If expressed in amperes, all currents in an equation must be reduced to the basis of the same winding. Expressed in any of these terms, the current in a winding is a direct measure of the volt-ampere load or power in that winding and may therefore be expressed also in volt-amperes, that is, as the current corresponding to the stated volt-amperes. All equations will be understood to be true vectorially.

A pair of independent but simultaneous load currents, Is in winding 3 and I4 in winding 4, may be resolved into two components; one component having identical numerical value and phase in both windings; the second component having the same value in both windings but opposite phase to each other, as follows:

Through mathematical investigations, I have found that the currents I1 and I: in windings I and 2, respectively, corresponding to the currents Ia and 14, in windings 3 and 4, respectively, in-

by the three terms on the right of each one of the equations as follows:

The negative signs in front'of the brackets arise from the consideration that the vector sum hence, the balanced share of each primary winding in the total load of the transformer.

The second term in Equations 3a and 4a,

namely,

negative in winding I and positive in winding 2, is an exchange or circulating current between those two windings, and, as indicated, is a function of the total output of the transformer independent of its division between windings 3 and 4.

The third term in Equations 3a and 4a,'

namely,

with opposite signs in windings I and 2, is also an exchange or circulating current between those two windings, but thiscirculating current is a function of the difference between the currents of windings 3 and 4, and is independent of the total output of the transformer, while the second component .was seen to be a function of the total output'independent of its division between windings 3 and 4. It is thus seen that an unequal division of load current between windings I and 2 may be conceived of as the resultant of the superposition of a balanced load current having H volve three important components, as represented the same sign, that is, flowing in the same direction (in or out). in both windings, and a circulating current, with opposite signs (flowing into one, and out of the other, winding) and that this circulating current in its turn can be resolved into two components; one dependent on total load and independent of the unbalance in the secondaries; the other,dependent on the unbalance in the secondaries and independent of the total load.

It may be observed that the third term, associated with k" in Equations 3 and 4, is exclusively characteristic of transformers having at least four windings and is absent in those with fewer windings.

The significance of the foregoing conceptions for the most advantageous operation of electrical systems involving multiwinding transformers of four or more windings may be realized in accordance with my invention by considerations as follows:

(A) If in Fig. 1, the circuits of windings I and 2 have equal volt-ampere capacities and it is desired to operate them with minimum total loss and minimum heating of the windings, the constants k and k" of the network should be zero, in which case, I1 and I2 will be alike independen of any unbalance inIz and I4.

(B) If, as further illustration, windings I and 2 have unequal capacities, or, if for any other reason, it is more advantageous to maintain I1 and I2 unequal but at a constant ratio to each other independent of the ratio of I: to I4, then it is necessary that the constant k" be zero and it an appropriate finite value.

(C) If, as a still further illustration, it is desired toreduce the short-circuit difl'lculties on the system by requiring that winding I exclusively shall furnish the load in winding 3, and winding 2 exclusively that in 4, then it will be seen that the constant It must be zero and It" must be unity.

(D) Finally, in the general case, the most advantageous operation of the system may demand that the unbalance between I1 and It for balanced loads in windings 3 and 4 be a certain finite amount, represented by k=c, and for maximum unbalanced loads an amount represented by k=c and k"=d,

loads in another pair of windings, such as 3' and I, in arrangements such as is shown in Fig. l and the other figures of the accompanying drawing and their various possible modifications.

I find that if it is desired that I1 and I: in the system shown in Fig. 1 be such as correspond to a value of k in Equations 3 and 4 equal to c, and k" equal to 41, this result can be secured inherently by adjusting the leakage impedances, Z12, Z13, Z14, Z2: and Z24 f the various pairs of the four windings of the transformer corresponding to the digits of the subscripts of the Zs in accordance with equations as follows:

I use the term leakage impedance" in its wellrecognized sense in the transformer literature, and wish to imply particularly the effective value thereof measurable at the circuit terminals if subject to modifying elements not normally a part of said leakage impedance. The reactances or impedances referred to herein are those reactances and impedances which the transformer offers to load currents but not those which apply to magnetizing currents. These impedances to load current are sometimes referred to as load reactance or load impedance but herein they are referred to as leakage reactance or leakage impedance in accordance with the common practice in transformer literature. It is well known that the power or kilovolt-amperes flowing between the windings l and 2, for example, must overcome the leakage impedance Z12. The various leakage impedances herein referred to are thus identified by Z with the digits of the subscripts corresponding to the windings involved. The values of the various leakage impedances in these and other equations may be expressed in ohms. If so, all of them must be reduced to the same voltage or turn basis, as well understood in the art. They may also be, and are preferably, expressed in "per unit values, based on a common reference load, a very convenient method of expression now in considerable use in transformer literature.

As the calculation of and design for specified leakage impedances is common knowledge among transformer engineers, these equations are sumcient to enable any one skilled in the art to design and build transformers having the characteristics under consideration.

It will be observed that Equations 5 and 6 offer only two limitations to the relationships of the five leakage impedances involved. They thus disclose not only how the desired result may be secured, but also the maximum degree of liberty in design which the designer may enjoy in securing those desired results; for, by a well-known algebraic theorem, two equations involving more than two independent variables (the leakage impedances in the present case) admit of an infinite number of solutions; and, therefore, there are an infinite variety of arrangements of four windings permitting their leakage impedances to satisfy the conditions of Equations 5 and 6.

It follows from Equations 3 and 4 and 5 and 8 that,ifthepowersinwindings i andiareto be balanced under all conditions of loading of windings I and l, the leakage impedances are to be adjusted in the relationships simultaneously as follows:

Hence, by elementary algebra, k'=%. and by Equations 5 and 6 the leakage impedance must be in the relationship (2.. -z..) (Zn 4..) =0

Obviously the two requirements of Equations '7 and 8, or 9 and 10, can be met'by the leakage impedances involved in an infinite variety of ways, and thus these equations disclose the maximum amount of freedom which the designer may enjoy in securing the characteristics mentioned.

Fig. 2 illustrates a modification of Fig. 1 in which the connections of windings I and I to bus I are made through lengths of line or cables oflering appreciable impedances, or through special impedors, such as for limiting short circuits or assisting in parallel operation or for other purposes, and represented in Fig. 2 by impedance l3 offering an impedance Z in series with winding 1, and impedance i4 offering an impedance Z" in series with winding 2. The impedances Z' and Z may have any vector value. It will be seen that the connection is equivalent to parallel operation of windings l and 2 with the introduction of external impedances into the paralleling loop.

I have discovered that in this modification, a desired division of power between the circuits of windings l and 2, corresponding to specified values of k and k" in Equations 3 and 4, may be secured by adjusting the leakage impedances of the windings in accordance with the following equations:

Evidently, if the internal impedances Zn, Zu, etc. are expressed as per unit values, then the external impedances should'also be so expressed.

Fig. 3 illustrates, again schematically, in a conventional one-wire diagram, a modification of Fig. 2 in which an additional voltage, which we may designate here as AE, is introduced into the loop by means of an auxiliary transformer, shown here as having two windings It and It, to further influence the division of power in the two branches of the loop, corresponding to windings land 2. Winding I6 of the auxiliary transformer is a secondary winding and is connected in series with the loop 9-8I0. Winding I of the auxiliary transformer is a primary and is excited from bus 8 through line H and a conventional tap-changing mechanism I8 shown in the figure very schematically as a movable arrow. It-will be apparent to those skilled in the art that any known method andmechanism for changing'the' magnitude, or the phase, or both -the magnitude and the phase, of the voltage AE introduced into the" loop through winding I 6,

may be utilized without departing from my invention in its broader aspects. The equivalent of AE may also-be obtained by unbalancing the ous quantities involved are expressed in "per unit values and provided it is understood that (Em-E) corresponds to AE, E20 corresponds to the common voltage of circuits I and 2 of Fig. 3,

Z and Z" correspond to the total external impedances respectively in series with I and 2,

. inclusive, of the corresponding generator impedances.

Y second element. Therefore, in speaking of parallel operation, I do not wish to be understood as restricted to circuits of identical voltage rating conductively connected in parallel, but as meaning broadly any arrangement in which the cir- In these equations, if the T5 are expressed in amperes, the Zs will be in ohms and the AE in volts, all, expressed in terms of the same wind- .ings or, as indicated above, all may be expressed q preferably in per-unit values. case, AE also will be a vector.

In the general g It will be seen from theseequations that any desired ratio of I1 to -Iz,-not otherwise inherent in the network, may be forced by suitable choice of AE. Insuch a case, the present invention is directed to such an adjustment of the leakage f-impedances of the windings as leads to the use of the minimum or otherwise most advantageous va lue ofAE and most economical equipment to furnish that AE to the system. Thus, given the most advantageous values of I1 and I2 correspondg to ;the -load conditions I: and I4 to which indingsil and 4 may be adapted to be subjected, we may determine by-Equations 11 and 12 the leakage .impedancevalues which will give this without the benefit of AE. If the required combination of. impedance values is disadvantageous from the standpoint of other requirements of vv the system, a set of compromise values are chosen forthe impedances and with their aid k and k" --are calculated by Equations 11 and 12. Thus,

having the values of the (Us, of the (Z)s, and

of the ,(k)s of Equations 13 and 14, the value of the necessary AE, as the single unknown defined by those equations, is readily calculated by elementary mathematical methods. Without the benefit of this method, unnecessarily large values of AE and equipment to furnish it will have to be provided to make certain that a desired division of power can be secured. Alternatively, given the desired relationship of I1 and I2, and the available AE, these equations define the necessary relationship of the various impedances to secure the desired results.

Fig. 4 shows a modification of Fig. 2 in which windings I and 2 are connected to independent generators I9 and 20 respectively instead of a common bus. For the purpose of the present invention, the system of Fig. 4 is completely equivalent -to that of Fig. 3, and the same equations as apply to Fig. 3 apply also to Fig. 4 irrespective of whether generators I9 and 20 have similar or different voltage ratings, provided that the varicults under consideration are able to interchange or circulate power, vectorially if necessary.

Evidently, if the generators I9 and 20 are of the same voltage rating and their busses connected together ahead of the transformer windings I and. 2, the resulting circuit will be equivalent to that of Fig. 1 or Fig. 2; and therefore, Figs. 3 and 4 may also be considered as different operating connections of one and the same system arranged in a flexible bus-sectionalizing scheme. Viewed particularly in this light, it will be seen that the adjustment of the leakage impedances of the four-winding transformer may b not only very desirable but also necessary to secure a specified result of the kind described desirable under various bus-operating schemes.

The application of the present invention is not limited to the use of a four-winding transformer, but includes also those with higher number of windings as well.

Fig. 5 illustrates schematically the application of a six-winding transformer, as a modification of Fig. 2 by the addition thereto of windings 5 and 6, their respective series impedances 2I and 22, their common bus 23 and common load 24. The load currents in windings I and 2 are now the resultant of the superposition of their respective load currents corresponding to (Is, I4) and to (I5, I6) that is, first calculate the duty in windings I and 2, considering the windings I, 2, 3 and 4 as a four-winding transformer, and then again with the windings I, 2, Sand 6 as a four-winding transformer; and combine the two results. If the distribution of load in windings 5 and 6 are desired, similar calculations as described above are made treating windings 5 and 6 as if they were the windings I and 2 of the foregoing equations, taking them first with one pair of the other windings (say 3 and l) as a four-winding transformer and then with the remaining pair.

' In the light of the foregoing explanations, the generalization of the method to the n-winding transformer will be clear to those skilled in the art.

As an n-winding transformer involves leakage impedances, a. six-winding transformer involves fifteen leakage impedances, and the arrangement of the windings to secure a desired result of ,the type described tends to increase in freedom and complexity with increasing number of windings. Therefore, as an example of a very desirable case, I shall describe now a specific arrangement of the windings of a transformer having three pairs of windings to secure inherently equal power or load divisionv within each pair of windings when the pair in question is connected into a loop or the equivalent of a loop. as follows.

Fig. 6 shows in section a single-phase transformer with concentric windings, comprising a core N with two winding legs H and 21, and

three pairs of windings I and 2. I and I, and I is and 8 respectively. Winding I is wound around and distributed along core leg 26 exclusively. Winding 2 is wound around and distributed along leg 21 exclusively. Winding 2 comprises two coils connected in parallel, 2a wound around and distributed along the upper half of core leg 28, and 2b wound around and distributed along the upper half of core leg 21. Winding 4 comprises two coils in parallel, 4a wound around and distributed along the lower half of core leg 26, and

lb similarly on the lower half of core leg 21. Winding I comprises two cell; in parallel, Ia wound around and distributed along the upper half, and 5b around the lower half, of core leg 2|; while winding I is similarly arranged on core leg 21. In every case, coils connected in parallel are wound around the core in such directions as to be suitable for parallel connection, as is well known in the art.

This arrangement of the three pairs of windings assures that the division of load between the two branches of a loop connected to any one of the pairs of windings, as paired above, will be equal and independent of the division within either one of two pairs the remaining pairs of the windings. This can be verified as follows:

By symmetry,

and therefore k and k", by Equations' md 6 are zero for the two pairs of windings l and 2, and 2 and 4. Therefore, the division of load in I and 2 will be equal and independent of any unbalance of load between 2 and 4.

Considering windings I and 2 in combination with windings I and I. it will be evident from symmetry again that Zas=Z1e (16) and That It" (Equation 6) is also zero for the present case may be verified as follow. Considering the reactance components of the various impedances,

because is substantially proportional to the insulation distance 81: between windings I and I, which is of circuits connected to distance Sm between I and la, plus the insulation distance Sam between 3a and Ia:

u su m +51.

The leakage reactance between windings 2 and I is substantially proportional to the sum of the insulation distances Sm (between 2 and lb, which distance is the same as Sm by symmetry) and Sam (between Ia and Ia), and therefore The foregoing statement about follows from the fact that a transformation of power from 2 to I takes place practically entirely then Xis=xac (22) It may be shown by similar reasoning that Z1! is substantially equal to Z20, and the conclusion follows that :s- .u) :e'- m) k 22,, 0 Division of load between these windings l and 2 when connected in parallel or in a loop, or operated in any manner making it possible for them to exchange current or power, is therefore on a basis of equality independent of any unbalance of load in the other pairs of windings.

The law governing the division of load between a pair of windings of a transformer is dependent on their ability to exchange or circulate power and not on their function as primary or secondary; so, in Fig. 5, in whichl and 2 are primaries, I and I secondaries, the division of load within each pair is determined by the same mathematical law. Accordingly, the analysis made in the foregoing. showing the inherent tendency of the transformer to balance the voltamperes in the pair of windings I and 2 when allowed to interchange power, may be repeated 6 similarly for the pair I and I, or I and I, of

Fig. 8, and the same conclusions will be reached. namely, that the transformer will inherently tend to maintain equal volt-amperes in each branch of any one of the pairs of windings as paired, regardless of load unbalance within either one of the other pairs.

If the inductively coupled windings of the transformer of Fig. 6 are shown by an equivalent conductively connected network of impedances representing the leakage impedances between pairs of windings, they take the form shown in Fig. 'I which shows very clearly that no current (or power) circulating within any pair tends to set up a circulating curmnt (or power) within evidently equal substantially to the insulation 7 W other P5115 It 18 to 59 noted mt 1' 8- 7 18 l Letters Patent of the United States is:

connection diagram like Figs. 1 to 5, inclusive, and not a vector diagram.

Another important characteristic of the system represented by Fig. "I is that no circulating current (or power) within any pair of the windings tends to unbalance the terminal voltage of any other pair; that is, unbalanced load in one of the pairs of the windings of Fig. 6 does not tend to unbalance the terminal voltages of another pair of the paired windings when the latter is not free to circulate power.

In the general case, Equations and 6, are modified as follows to give the componentsof voltage unbalance in I and 2, caused by arbitrary currents in I and 4, when circulation of power between I and 2 is prevented:

Here, Al! is the voltage unbalance caused exclusively by the balanced components, and All" that caused exclusively by the unbalanced components, of the currents in I and 4.

Frequently, it is desirable that such voltage unbalancing eflect. be absent, while sometimes it is desired that the voltage of one of the circuits increase with respect to that of another under specified conditions of loading, and Equations 25 and 26 show how either kind of reof transformers with four or more separate wind-' ings for clarity of expositio of its principles, it will be evident to those s led in the art that the various windings need not be separately insulated but may have parts in common as autotransformers, and that the various equations and relationships specified in the foregoing apply equally in all cases if the values of the various impedances involved in those equations and relationships are the values efi'ective at the terminals. of the respective circuits. Therefore, in all my references to transformer windings I wish to be understood broadly as including autotransformer windings as well as those which are separately insulated.

Furthermore, while I have shown and described my invention by means of particular representative embodiments thereof, it will be obvious to those skilled in the art that many changes and modifications may be made in them without departing from my invention; and I, therefore, aim to cover in the appended claims all such changes and modifications as fall within the true spirit and scope of my invention.

What I claim as new and desire to secure b 1. A multiwinding alternating current transformer having at least four windings designated respectively I, 2, I, and 4 in which the leakage impedances of said windings are prearranged to have the relationship wherein Z13, Z14, Zn and Z24 represents respectively the leakage impedance of each of the winding pairs corresponding to the digits of the subscripts of the letter Z, so as to cause a predetermined division of current fiow between one pair of windings independently of the relative loading of the other windings when said one pair of windings is connected for parallel operation and said'other windings are connected to be loaded simultaneously and independently of each other.

2. A multiwinding alternating current transformer having at least four windings designated respectively I, 2, 3, and 4 in which'the leakage impedances of said windings are prearranged to have simultaneously the two relationships wherein Z12, Z13, Z14, Z2: and Z24 represent'respectively the leakage impedance of each of the winding pairs corresponding to the digits of the subscripts of the letter Z,'so as to cause the current in one of the windings of one pair of said windings to be substantially proportional to therespectively I, 2, 3, and 4 in which the leakage impedances of said windings are prearranged to have simultaneously the two relationships n 1a) i 24 14) and (Z23 -'Z13)' (Z24 '-Z14) 20 wherein Z13, Z14, Zn and Z24 represent respectively the leakage impedance of each of the winding pairs corresponding to the digits of the subscript of the letter Z, so as to cause an equal division of load between one pair of windings independently of the relative loading of the other windings of said transformer when said one pair of windings is connected for parallel operation and when at least two other of said windings are loaded unequally.

4. In combination, a multiwinding alternating current transformer having at least four windings generally designated I, 2, 3 and 4 and having the leakage impedances designated Z111, Z114, Z14, Zn and Z24 representing respectively the leakage impedance of each of the winding pairs corresponding to the digits of the subscripts of the letter Z prearranged to cause a division of load between windings I and 2 when operated in parallel to be in the ratio of (1+k') to (1-70) for a predetermined loading of windings 3 and 4, and a difierent division of load corresponding to the super position of a circulating power in said windings I and 2 equal to k" times one-half the difference between the loads of windings 3 and 4 when operated with unbalanced loads, said transformer leakage impedances being proportioned in accordance with the simultaneous equations 5. A multiwinding alternatingcurrent transrormerhaving at least four windings designated respectively I, 2, 3, and 4 in which the leakage impedances of said windings are prearranged to have simultaneously the two relationships n u) n -Z11) and (Z2: -Z1|) u '11) wherein Z13, Z14, Z2: and Z24 represent respectively the leakage impedance of each of the winding pairs corresponding to the digits of the subscript oi the letter Z, so as to maintain the terminal voltages of two of its windings balanced independently oi the relative loading the remaining windings when said remaining windings are loaded.

6. A multiwinding alternating current transformer having at least four windings and generally designated respectively I, 2. 3 and 4, in which the leakage impedances 01' said windings have simultaneously the two relationships 2; 1s) n 14) g0 wherein Z13, Z14, Zn and Z24 represent respectively the leakage impedance of each of the winding pairs corresponding to the digits of the subscript of the letter Z.

7. A multiwinding alternating current transformer having at least four windings designated respectively I, 2, 3, and 4 in which the leakage impedances are prearranged to have the relationship wherein Z11, Z14, Z2! and Z24 represent respectively the leakage impedance of each of the winding pairs corresponding to the digits of the subscripts or the letter Z, so as to render the difference between the terminal voltages of a pair of said windings independent of any load unbalance in the remaining windings when said remaining windings are loaded.

8. A multiwinding alternating current transformer having at least four windings and generally designated respectively I, 2, 3 and 4, in which the leakage impedances of saidwindings have the relationship wherein Z13, Z14, Zn and Z24 represent respectively the leakage impedance oi each of the winding pairs corresponding to the digits 0! the subscript of the letter Z.

9. A multiwinding alternating current trans former having at least four windings and generally designated respectively I, 2, 3 and 4 in which the leakage reactances of said windings have the relationship v- 13) (K -X 20 10. A multiwinding alternating current transformer having at least four windings designated respectively I, 2, 3, and 4 in which the leakage impedances are prearranged to have simultaneously the two relationships wherein Zn, Zn, Zn and Z24 represent respectively the leakage impedance of each of the winding pairs corresponding to the digits of the subscripts or the letter Z, so as to cause the diiierence between terminal voltages oi two of its windings to vary proportionally to the difference in the loads or two of its other windings when said other windings are loaded.-

11. A multiwinding alternating current transiormer having at least four windings and generally designated respectively I, 2, 3 and 4 in which the leakage impedances oi said windings have the relationship 1 wherein Z13, Z14, Zn and Z24 represent respectively the leakage impedance of each of the winding pairs corresponding to the digits of the subscript 01 the letter Z.

12. man alternating current distribution system, a generating source, a bus member connected to said generating source, a pair oi distribution branch circuits connected to said bus member, the total series impedance of said branch circuits being Z and Z" respectively, a multiwinding transiormer having two windings generally designated I and 2 which are connected respectively to said branch circuits and having two additional windings generally designated 3 and 4 which are connected to be loaded simultaneously and unequally, said two branch circuits having a most advantageous division of power in the ratio of (1+k') to (1-k') when said windings 3 and 4 are equally loaded, and a different most advantageous division of power corresponding to the superposition of a circulating power in said two branch circuits equal to k times one-half the difference in the load of said windings 3 and 4, the leakage impedances Z12, Z13, Z14, and Zn, and Z24 which represent respectively the leakage impedance of each of the winding pairs corresponding to the digits oi the subscripts of the letter Z having the two relationships 13. In combination, a multiwinding alternating current transformer having at least four windings generally designated I, 2, 3 and 4 and having leakage impedances designated Z12, Zn, Z14, Zn and Zz4 representing respectively the leakage impedance 01' each 01 the winding pairs corresponding to the digits of the subscript of the letter Z, an advantageous division of load between windings l and 2 when operated in parallel being in the ratio oi! (1+k) to (l*-k') for equal loading of windings 3 and 4, and a, different advantageous division of load corresponding to the superposition of a circulating power in said windings l and 2 equal to 7:" times one-half the difference between the loads of windings 3 and 4 when operated with unbalanced loads, an impedance Z connected in series with winding I, and an impedance Z" connected in series with winding 2, said transformer leakage impedances and said series impedances Z and Z" being proportioned in accordance with the simultaneous equations n 1a) (Z24 -Z14) 14. A multiwinding alternating current transformer having three pairs of windings designated respectively I and 2, 3 and 4, and I5 and 6,111 which the leakage impedances of said windings are proportioned to have the following relationhip n 10 4 20 l6) wherein Zn, Z14, Z15, Zn, Z24, Z25, and Z20 represent respectively the leakage impedance of each and of the winding pairs corresponding to the digits of the subscripts oi the letter Z, so as to make the ships 2: 1:) 24 10 wherein Zn, Z14, Z15. Z23, Z24, Z2: and Z20 represent respectively the leakage impedance of each of the winding pairs corresponding to the digits of the subscripts of the letter Z, so as to maintain the terminal voltages of a given pair of windings balanced independently of the condition of load unbalance within any one of the other pairs of windings.

16. A multiwinding alternating current transformer comprising a magnetic core having two winding legs, a pair of similar windings arranged one on each winding leg and distributed along substantially the full winding length of said winding leg, a second pair of windings arranged symand and

prising a magnetic core element, a pair of windings so disposed on said core element as to provide high leakage reactance between said pair of windings when not coupled through other windings, a second pair of windings on said core element and so disposed as to provide high leakage reactance between themselves and also between each one of them and each one of said first pair .of windings, when not coupled through other windings, and a third pair of windings arranged on said core element and so disposed as to provide high leakage reactance between each one of said third pair of windings and one of the first pair of windings when not coupled through other windings, saidsecond pair of windings so disposed as to couple closely said first pair of windings with each other and said third pair of windings with each other, and said third pair of windings so disposed as to couple closely said second pair 0! windings.

18. In an alternating current distribution system, two circuits in said system, a multiwinding transformer having at least four windings generally designated I, 2, 3 and 4 and having leakage 5 impedances designated Z11, Z13, Z14, Z2: and Zn representing respectively the leakage impedance of each of the winding pairs corresponding to the digits of the subscript of the letter Z, an advantageous division of load between windings I and 2 when operated in parallel being in the ratio of (1+k') toil-k) for equal loading of windings 3 and 4, and a diil'erent advantageous division of load corresponding to the superposition of a circulating power in said windings I and 2 equal to k" times one-half the difference between the loads of windings 3 and 4 when operated with unbalanced loads, said windings I and 2 being con.- nected to said two circuits in a manner to permit a circulation of power between said windings I 40 and 2 and said circuits, variable impedances Z andZ" connected external to said winding pair I and 2, respectively, to be traversed by said circulating power, means for loading said windings 3 and 4, means operatively connected with winding pair I and 2 to provide a variablevoltage AE for modifying the power in said windings I and 2 irrespective of the condition of loading of said windings 3 and 4, said transformer leakage impedances being so proportioned and said variable impedances Z' and Z" being so adjusted that the currents in windings I and 2 will have the following relation metrically on said two winding legs, each winding where I1 and I: are the currents of windings I including two parts in parallel, one of said parts of one of said pair of windings being distributed along one-half of one of said winding legs and the second part along one-half of the'other leg, the two parts of the second winding of said second wherein pair of windings being distributed respectively on the remaining halves of said winding legs; and a third pair of windings-arranged one on each one of said winding legs, each winding including two parts in parallel and distributed respectively along the two parts of the second pair .of windings on the same core leg; said first and third pairs of windings being disposed on opposite sides of said second pair of windings.

17.,An alternating current transformer comand 2, Is and I4 are the currents as windings I and 4, Z is the leakage Impedance of the winding pairs indicated and AE is the voltage derived from the means to provide said variable voltage, and

ALEXISN. GARIN.

Certificate of Correction Patent No. 2,264,836. December 2, 1941. ALEXIS GARIN It is hereby certified that errors appear in the printed specification of the above numbered patent requiring correction asfollows: Page 1, second column, line 21, for drawing read drawings; page 2, first column, line 16, for mathematic read mathematical; page 5 first column, line 65, for follow read follows; line 69, for 1 ,211,, read 2 mg and line 72, for i read 1: and second column, line 4, for i read Zr l1 r 1e 6, for in, read 25 line 14 for 2 22,, read 2 22, and line 16, for i read page 6, second column, line 5, claim 1, for represents read represent; and that the said Letters Patent should be read with these corrections therein that the same may conform to the record of the case in the Patent Ofiice.

Signed and sealed this 20th day of January, A. D. 1942.

[SEAL] HENRY VAN ABSDALE,

Acting Commissioner of Patents.

Certificate of Correction Patent No. 2,264,836. December 2, 1941. ALEXIS N. GARIN.

It is hereby certified that errors appear in the printed specification of the above numbered patent requiring correction as-follows: Page 1, second column, line 21, for drawing? read drawings; page 2, first column, line '16, for mathematic read un afe!- read 13 :1 5; and line 72 for 12 read 2: and second column, line 4, for 92 readZ' lme 6, for i read 5 line 14 for iugifl read zzmgz and line 16, for 3 read 2 page 6, second column, line 5, claim 1, for represents read represent; and that the said Letters Patent should be read with these corrections therein that the same may conform to the record of the case in the Patent Office.

Signed and sealed this 20th day of January, A. D. 1942.

HENRY VAN ARSDALE Acting Gommzssioner ofPatents.

mathematical; page 5 first column, line 65, for follow read follows; line 69, for v

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