Anti-harmonic transformer

[57] ABSTRACT

Devices for eliminating in a three-phase voltage transformer T, separating two networks A and B the voltage harmonics preexisting within the three phase voltage feeding A and detrimental to B, or the current harmonics generated by B and detrimental to A. The devices include single phase transformers, the primary windings of which are “delta” coupled and the secondary windings of which are “star” coupled, the angles determined by the legs of the triangles and of the stars exhibiting unique values, together with single phase autotransformers for connection to the A and B networks. When eliminating only current harmonics, T need only be constituted of two single phase transformers the primary secondary windings of which are in quadrature together with single phase transformers, the windings of which are connected to specific current taps provided on the above-mentioned transformers. They can be used in installations for electrochemistry, electrometallurgy, power distribution of d.c. current and for installations of static power conversion.

Claims, 11 Drawing Figures

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PATENTED JUH 20 1372

3,671.901

SHEET 1 OF 4

FIG.I

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FIG.2

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PATENTED JUN 20 1972

3,671,901

SHEET 2 OF 4

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F/G.5

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PATENTEDJUH20 137?

3,671,901

SHEET 3 Of 4

FIG.6

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<img file="US3671901A_D0009.tif" />

PATENTED JUN 201972

3,671,901

SHEET U OF 4

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3,671,901

ANTI-HARMONIC TRANSFORMER

DETAILED DESCRIPTION

BACKGROUND OF THE INVENTION

The present invention relates to polyphase voltage transformers for removing voltage and current harmonics from electrical networks which are connected by the transformers. For example, if the transformer separates a first from a second network with the power passing from the first to the second, it can protect the second network from the harmonics existing in the first network. Similarly, if the second network includes nonlinear elements which generate current harmonics, the present invention prevents such harmonics from being transferred to the first network.

In industrial practice, electrical polyphase voltage transformers are conventionally provided with “symmetrical” windings whether or not they include single phase elements with independent circuits and star or polygon coupled electrical circuits, or include windings arranged on a single magnetic circuit with free or forced flux. They generally include a primary winding and a secondary winding for which are used conventional connection arrangements such as “star”, “delta”, “mesh” and so forth.

Depending upon the connection arrangements selected for the three-phase transformers, the third harmonics and their multiple can normally be eliminated. For instance, if both the ²³primary and secondary windings are star coupled and their respective neutral points insulated, the flux components produced by current third harmonics and their multiple are prevented from circulating. Moreover, if for example the secondary winding is delta coupled, the electromotive force ³⁰includes a frequency three times as high as the fundamental and generates in the delta circuit a current whose frequency is also triple, which almost completely suppresses the third harmonic and supplies the necessary ampere-turns for a correct compensation of the flux within the magnetic cores, whether ³⁵the transformers are free or forced flux types.

This latter property is, furthermore, used more particularly for “star-star” coupled large transformers with delta arranged tertiary windings.

Therefore, in most cases only the third harmonics and their multiple are eliminated through the above mentioned conventional couplings.

SUMMARY OF THE INVENTION

An object of the invention is to provide an improved apparatus for eliminating harmonics in single and polyphase transformers.

The devices according to the invention eliminate harmonics of all kind without restricting such elimination to third har- 50 monies and their multiple. These devices are of two types: those related to the devices for eliminating current harmonics generated by nonlinear network impedances fed back to the power supply and those related to the devices for eliminating both the voltage harmonics generated by the power supply for 55 the network it feeds or the current harmonics generated by the lack of linearity of the network impedances.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 and 2 are schematic diagrams of transformer 60 couplings in accordance with this invention;

FIG. 3 is a geometric representation of the relationship between windings determined in accordance with this invention;

FIG. 4 is a schematic diagram of transformer windings geometrically arranged in accordance with this invention;

FIGS. 5 through 8 are schematic diagrams of geometric arrangements of transformers connected in accordance with this invention;

FIG. 9 is a geometric representation of the relationship between windings for eliminating voltage and current harmonics in accordance with the principles of this invention; and

FIGS. 10 and 11 are schematic diagrams of yet other windings geometrically arranged to eliminate voltage and current harmonics. 75

With respect to the first above mentioned type, the present invention embodies with a three-phase system, a transformer T made of two single phase transformers 1 and 2 the primary and secondary windings of which are electrically intercoupled in a “quadrature” (see FIGS. 1 and 2).

The “quadrature” coupling hereafter referred to is actually the coupling characterizing the three phase windings of the so10 called “Scott” configuration, one of the windings having V3I2 times less winding turns than the other, and one of its ends being connected to the middle point of the other, both thus including the altitude and the base of an equilateral triangle, according to the classical conventional representation.

This “quadrature” coupling for the couplings 1 and 2 has two possible arrangements: in the first, both transformers 1 and 2 have the same transformation ratio β equal to the transformation ratio of T; in the second, the transformers respectively have for a transformation _r a

βζ = — β

V3 β being the transformation ratio of T.

Transformers 1 and 2 are provided with intermediary current taps H and h on their respective windings and, between these taps, “filtering” transformers are provided.

According to FIG. 3 (related to the arrangement of FIG. 1), the triangles ABC and abc have centers O and 0 which stand for the primary and secondary voltage triangles and their respective origins, two regular pentagonal contours centered in O and 0 can be formed having particular vertices A₅, B₅, C₅, and &lt;z₅, fc₅, c_s. These vertices are precisely carried by AH and BC for the first and by ah and be for the second transformer.

In accordance with transformer theory, the voltages across the terminals of a winding or part of it can be shown as the voltage diagram of the transformer and, similarly the segments shown as the diagram of voltages may represent the windings or part of windings at the terminals of which the voltages represented by these segments can be recovered.

Segments A₅B_S, A₅C₅, a₅b₅, a₅c_s, which are seen in FIG. 3, represent the windings of the single phase transformers linking the unique points A₅, B,, C₅, a₅, i&gt;„ c₅.

FIG. 4 is a diagrammatical representation of the device after both transformers have been arranged, the primary and secondary windings respectively connecting the unique taps bearing subscript 5. If a system of three phase sinuoidal voltages is applied to ABC, a system of voltages which are also three phase and sinuoidal will appear at abc; if moreover, the network fed in abc includes nonlinear impedances (rectifiers, thyristors or the like) the feeding currents will comprise, apart from the fundamental harmonics, all orders and, particularly, the fifth harmonics and their multiples.

The wound circuits A₅B₅C₅ and a^cj, taking into consideration the unique points or positions of the tap of subscript 5, have the property of only including, so far as currents with a frequency of five times the fundamental frequency is concerned, homopolar currents which are phase equal currents to which the impedance presented by A₅B₅C₅ and ajb^ is very low.

In other terms, the presence of the “filtering” transformers (A5B5 - a5b5) and (A5C5 - a5c5) removes from the network the current harmonics of fifth order and their multiples. It is to be noted that removing a single phase transformer as (A5C5 aScS) does not change the result so that the fifth harmonic 70 which is sought to be eliminated can be completely suppressed by a single phase transformer with primary AsB₅ and secondary^»·

This result which has been shown for the fifth current harmonic can be extended to any harmonic of sequence i (i odd), the foregoing description applying to pentagonal con3,671,901 tours and being applied to the polygonal regular contours having i sides, respectively centered in O and o, two vertices of which are respectively carried by the sides BC and be of the triangles ABC and abc and a third vertex of which is itself located respectively on the segment AH and on the segment 5 ah.

In other terms, the current harmonic of sequence i can be removed by embodying — according to FIG. 5 — a filtering single phase transformer (A^ - a(b₍), respectively, at the level of the primary and secondary windings of the transformers 11 and 12, between the intermediary taps A,, B₍, a_t, b_t, the positions of which on the associated primary and secondary voltage diagrams are such that OA₍ = OB_f, oa,=ob, and the angles formed by OA, and OB₍ and oa, and ob, are equal to a whole number of 2 ir/i radians. This condition can be written in accordance with the following expressions:

HAi^hai_l/l+--------\

HA ha 31 cos (2fe+l)y) in which k is a whole number or null

HB-, hb·, 1 , ,, . ,. π HB ⁼ hS=^^k+1)i

The geometrical segments thus outlined represent for the same coil the number of turns of the winding sections they stand for.

Using k—0, these expressions lead to a simple solution, viz.:

Without hampering the efficiency of the device, the representation of it is thus simplified.

One may note that the arrangements shown at FIGS. 5 and 6 extend to the harmonic of sequence (, the above mentioned property characterizing the delta coupled windings of conventional three phase transformers with respect to eliminating third order current harmonics and their multiple.

The “anti-current harmonics” three phase transformer is thus characterized by the assembly of the two transformers 10 11-12 and 61 -62 and the associated single phase transformers (A,B₍ - a,b,) as described hereabove.

This will eliminate all current harmonics of any sequence (generally odd) liable to be generated by nonlinear impedances fed from the network.

A balanced three-phase system is liable to cause the appearance of current harmonics of sequences 3,5,7,11,13,17,19, etc. each one susceptible to being eliminated by the method hereabove described. However, in order to embody the smallest possible number of single phase transformers one can limit the same, although sometimes with a slight efficiency drop of the device, to eliminate harmonics by units of 2. For instance the 5th and 7th harmonics can be substantially reduced through the embodiment of a single ₂₅ transformer (Α,Β, - α,6_β) linking the taps Α», B_e, a„ b_t, such

HAt₌ha_i=\ f 1 \ &lt;3+2 HA ha 3 \ ~^cos π/6/ 3^/3 according to the arrangement of FIG. 5

HBt hbt 1 or such as:

HA,_1 ( 1 \ V3+2

HA 3 \ ' cos π/β/^- 3_V3 according to the arrangement of FIG. 6

-HB^^⁹^-⁷³

HB_t_bb₆HAt bat *ⁿ replacement for the two transformers (A₅B₅ - α/&gt;_ύ) and (A₇B₇-a_;Z&gt;₇) theoretically required.

Similarly, the harmonics 11 and 13 could be substantially eliminated by the use of a single phase transformer linking the taps having the subscript 12, harmonics 17 and 19 being in 50 turn eliminated by a single phase transformer of subscript 18 and so on.

Furthermore, for instance, harmonics 13 and 17 could be damped by a transformer linking the taps of subscript 15.

Thus, and generally speaking, two harmonics following one 55 another could be eliminated through a single phase transformer the subscript of which is equal to half the sequence sum of these harmonics.

It is obvious that this invention may apply to any polyphase system and is not restricted to three-phase systems; in particu60 lar, when the “anti-current harmonic” transformer also multiplies the number of phases.

FIG. 7 illustrates this property showing the transformation of a conventional classical three phase system to a five-phase system: the transformer 71 comprises three windings, viz.: AH 65 at the primary, a,h, and at the secondary; the transformer 72 comprises two windings, viz.: BC at the primary and be at the secondary. Embodying suitable single phase transformers across the taps at the unique positions, according to the same principles as above outlined, allows eliminating cunent har70 monies the number and the importance of which are reduced by the increase in the number of phases.

Lastly, the method also suits the “teritiary” windings of power transformers if the components of the main windings (primary and secondary) of these transformers are similar to 75 that characterizing the above-mentioned T transformer comHAi₌hai₌y__1_\

HA ha 3\ . cos ir/i/

HBi hbi 1, ,.

and without hindering the efficiency of the apparatus the presentation with k = 0 is more simple, tg is the trigonometric tangent.

Applying the same type of mathematical approach for the arrangement shown in FIG. 2 also allows removing current harmonics of sequence i. In fact, the transformer (A₍B₍ - a,b,) is arranged according to FIG. 6 between the taps A₍B, at the primary and a,b, at the secondary winding; the tap b₍ extending from the winding b_o and the taps A₍, B₍, a,, b,, being so arranged that the triangles A₍B₍H₍ and a,b,h_t, with center o, are geometrically similar and that oa, is equal to ob,, it is possible under the same conditions as above to remove the harmonics of sequencer.

More specifically, the current taps A_t, B₍, a_t, b, between which the filtering transformer (A₍B₍ - a/&gt;,) is arranged are such (according to FIG. 6) that:

HAi—U i-i_____1\

HA 3 V cos(2i+l)r/i/ k being a whole number or null

HBi^bbt Ha·, ba·,

The geometrical segments thus outlined also represent for one and the same coil the number of turns of the winding sections they stand for.

Applying k — 0 in these expressions also leads to a simple solution, viz.:

Ha 3 \ ^cos π/ί/

HB, ba·, 1 . ,. HB~ ba HB. bbj HA-,~ba·,

3,671,901 posed of single phase windings respectively arranged in quadrature. It is possible to utilize tertiary type windings wound as the above mentioned transformers 71 and 72 on the same magnetic circuits as the preceding ones and on which intermediary taps of the A(B_f and a,b, types are also provided; single phase transformers (A₍B₍ - a,b,) link these taps in order to eliminate the current harmonics of sequence i, this arrangement constituting an extension of the principle of the transfer mers provided with three windings, one of which is delta arranged with a view toward eliminating harmonic 3.

The devices according to the second category set forth at the beginning of the description enable voltage and current harmonics of any / sequence to be eliminated. They embody three single phase transformers, as shown in FIG. 8, transformers which are 81,82 and 83.

The transformer 81 is formed by a primary A₍B₍ and a secondary a₍Z&gt;₍. The transformer 82 is formed by a primary A,C( and a secondary e&lt;c₍. The transformer 83 is formed by a primary B(C₍ and secondary 6(C₍.

The primary windings are delta coupled (dissymetrical) and the secondary are star coupled (also dissymetrical), with center 0. Feeding the primary windings A(B₍C( occurs through autotransformers AH and BC which are themselves power supplied in A, B, C. Intermediary taps are provided on these autotransformers the position of which are such that:

^i_l / . 1 \

Ha 3 \ ^Ψ cos (2/:+1) ir/(/

HB~HC~$^g(^2k+r&gt;

In these expressions k is a whole number or null and the outlined geometrical segments also characterize the modulus of the corresponding composite voltages.

The secondary windings are star coupled at 0 and the end sections afi, of the star are, according to FIG. 8, connected by a single phase transformer afi,; intermediary current taps b and c are provided on this autotransformer so that the end section 6, of the star and the points b and c form an equilateral triangle, the center 0 of which is the same as that of the triangle 0(6(0,. Similarly to the features of the devices described with relation to the first category, A₍, B₍, and C, represent the voltages at the diagram of FIG. 9 and, with relation to FIG. 8, the 3 particular vertices of a regular polygon haying i sides centered in 0. The transformation ratios of transformers 81, 82 and 83 are:

ob, _QCj _oai ΒιΟΓΟιΑΓΑιΒι as illustrated in FIG. 9.

The arrangement thus described is such that if the supply three phase voltage at A, B, C has a harmonic of sequence i, the current harmonics of sequence i earned by the primary windings of transformers 81, 82 and 83 are homopolar, this meaning that they are equal and respectively in phase. Consequently, the harmonic three phase voltages of rank i at the secondary winding of transformers 81, 82 and 83 are in phase and those respectively available at the secondary winding of transformers 81,82 and 83 are in phase and those respectively available at 6₍, 6 and c are equal with respect to modulus and phase. The composite voltages available across 6₍, 6, c at the secondary winding are consequently free from any harmonic of rank i.

The present apparatus is reversible, this meaning that fed with a three-phase voltage at 6₍, 6, c it will also exhibit at A, B, C a three-phase voltage free from any harmonics of rank i. Lastly, this arrangement can filter current harmonics of rank i in the same way as the devices of the above described first category.

Should several harmonics of the feeding voltage with ranks i, j . . . I have to be eliminated, the above described arrangements for eliminating the harmonic i are applied one after the other and a “series” arrangement is embodied which is characterized as follows:

Each harmonic can be eliminated through a set of three single phase transformers 81, 82 and 83, fed through adequate taps provided on the autotransformers AH and BC.

The secondary windings such as ca_t are series connected so as, one with the others the secondary windings such as oc₍ and also the secondary windings such as ob,. In that way, the primary windings of the type A₍B₍ are “parallel” arranged across the taps of the type A₍B, set on AH and BC whereas the secondary windings of the type ob, are series arranged in conformity with FIG. 10; a single phase autotransformer is inserted between the end taps a and c of the secondary winding, and this single phase autotransformer is provided with intermediary current taps b and c in the same position as set forth above.

Consequently the three phase voltage available across the terminals b,, b, c is free from the harmonics of rank i,j . . . I that were to be eliminated.

This “series” arrangement is likewise reversible and embodies 3n single phase transformers and three single phase autotransformers, n being the number of harmonics of odd rank and of prime numbers with relation one to the other that were to be eliminated.

It is possible to simplfy the device by noting in FIG. 11 that the secondary current taps b and c can merge with the end taps aj and q, provided certain conditions are met: this will happen if certain current taps of the type Aj are utilized exterior to the segment AH (see Fig. 11) so that the voltage triangle AjBjCj exhibits an obtuse angle greater than 2 π/3 radians. Under such conditions, adequate transformation ratios can be selected and polygons ocfi_} and oa^ can be built with the angle Cjoaj (FIG. 11) precisely equal to 2 ir/3 radians.

The devices according to the first category can be used for all polyphase networks(generally three-phase) which have to be protected from the influence of current harmonics. This influence from harmonics is always a drawback and often causes power losses through eddy current, overheating, resonances and overvoltages, operation instability, radioelectrical disturbances and so forth. Apart from particular cases where eliminating a harmonic of any determined sequence is the main object, it should be noted that the “anti-current harmonic” transformer can be used with or without conversion of the number of phases before rectifiers and power thyristors: the current harmonics .that the latter often generate are detrimental in a general way to the network through which they are fed. This is the case for certain installations such as batteries charging, traction, electrochemistery, electrometallurgy, power supply for radio transmitters, power distribution through high voltage d.c. current, and so forth.

The devices according to the second category can eliminate voltage and current harmonics. The “anti-harmonics” transformers thus defined are not only used for the application above-mentioned, but may also be used after certain generators supplying a periodical wave which is not purely sinuoidal such as inverters and static cycloconverters, particularly when those apparatus are assisted, that is when they feed an already existing network which commands frequency and voltage form.