US2071834A - Polyphase impedance drop compensator - Google Patents

Description

Feb. 23, 1937. E. L, HARDER 2,071,834 X POLYPHASB IMPEDANCE DROP co'urnusuon 7 Filed Dec. 13, 1935 I ig z wl 4'1 A /fl1: q a

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WITNESSES: INVENTOR Edwin L. Hrdgr.

Patented Feb. 23, 1937 UNITED STATES PATENT OFFICE Edwin L. Harder, Forest Hills, Pa, assignor to Westinghouse Electric a Manufacturing Company. East Pittsburgh, Pa, a corporation of Pennsylvania Application December 13, 1935, Serial No. 54,255

Claims.

My invention relates to alternating-current impedance drop compensators, and particularly to such compensators as used in connection with power transformers to derive high-voltage quantities from the low-voltage circuits of the transformers.

Such compensators commonly operate to produce compensating effects equivalent in magnitude to impedance eflects of the transformers but opposite in sign, which are added to the low-voltage quantities of the transformers to reproduce variables existing on the high-voltage sides of the transformers. If the transformer connections are such that phase voltages and phase currents are carried through the transformation without combinations between phases, the ordinary methods of compensation are directly applicable. However, transformer connections are frequently utilized which result in a different system of secondary polyphase variables because of combinations of phase quantities. In such applications, quantities which are present as components of a single primary variable, usually appear as components of a numher of secondary variables, and the duplication of primary variables by compensation methods is ordinarily not practical because of the excessive number of instrument transformers required. I have found, however, that by utilizing the symmetrical impedance relationships which can be obtained in commercial transformer installations, high-voltage quantities may be duplicated from the low-voltage transformer circults by means of comparatively simple instrument transformer apparatus, and with com paratively small error.

It is accordingly an object of my invention to provide a novel method of and apparatus for impedance drop compensation which will be applicable to polyphase transformer apparatus of the class in which a combination of phase quantitles or other change of polyphase dimensions accompanies the transformation.

Other objects of my invention will become evident from the following detailed description taken in conjunction with the accompanying drawing, in which Figure 1 is a diagrammatic view of a polyphase transformer and impedance drop compensator embodying my invention.

Fig. 2 is a vector diagram showing the relationship of voltages in the transformer bank of Fig. 1.

Fig. 3 is a diagrammatic view of a modified potential transformer arrangement for use in the circuit of Fig. 1, and

Fig. 4 is a diagrammatic view of a simplified impedance drop compensator which may be used in the practice of the invention.

Referring to Fig. 1 in detail, a polyphase highvoltage circuit I is connected to a polyphase lowvoltage circuit 2 by means of a transformer 3, shown as having star-connected high-voltage windings l with neutral ungrounded and deltaconnected low-voltage windings 5. The highvoltage windings 4 may be provided with a tapchanging device as indicated diagrammatically at 6.

The transformer 3 may be any suitable form of stationary induction apparatus capable of transforming polyphase power, such as a single polyphase transformer or a bank of singlephase transformers. It is essential, however, that the leakage impedance, on both primary and secondary sides, have substantially the same value as to magnitude and phase angle, in all phases. It is also desirable that the mutual impedance between primary windings and secondary windings be similarly symmetrical in all phases, although some variation of mutual impedance may be permitted without serious error.

A two-element power responsive device such as a wattmeter I is provided for m a polyphase power quantity, such as the total real power flow, of the circuit I. The wattmeter I is provided with the usual current coils 8 connected to be energized in accordance with phase currents of the high-voltage circuit by means of current transformers I0. The voltage or potential coils 9 of the wattmeter I are connected to be energized from the low-voltage circuit 2 by means of a pair of potential transformers I 2 and impedance drop compensators IS.

The potential transformers I 2 are each preferably so constructed as to produce two secondary voltage components of equal magnitude and to provide simultaneous adjustment of the ratios of these components to the voltage impressed on the potential transformer primary windings. For this purpose, I preferably provide a mid-tap IS on the secondary winding of each potential transformer l2 and adjustable end-taps II on the primary windings. It will be obvious, however, that other transformer arrangements having an equivalent function may be used.

The compensators I! may be of any suitable type, one example of which is disclosed in my copending application Serial No. 52,121, filed November 29, 1935, and assigned to the Westinghouse Electric 81 Manufacturing Company. Such compensators comprise a mutual reactance section l8, consisting of two windings on a common core (not shown), and a mutual resistance section comprising a resistor 20 and a low-voltage auxiliary potential transformer 2|. The adjustments of the reactance section l8 and resistor 20 may be similar to those disclosed in the abovementioned application but for simplicity have been omitted from the present drawing.

The compensators l3 are energized in accordance with line-currents of the low-voltage circuit 2 by means of current transformers 22, and serve to introduce voltages in the secondary circuits of the potential transformers l2 proportional to the voltages consumed by the leakage impedances of the power transformer 3, as explained in my c0- pending application mentioned above.

The operation of the above described apparatus may best be understood by considering the circuit analytically. In the following, capital letters are used to denote complex or vector quantities and lower case letters are used as subscripts. The conjugate of any vector quantity is denoted by the corresponding capital letter surmounted by a circumflex accent. Scalar quantities are denoted by a capital letter surmounted by a bar. To simplify the equations, it is assumed that the ratio of each star-connected primary winding of the transformer 3 to the corresponding delta-connected secondary winding is 1:1.

each phase of transformer 3, considered from delta side and assumed the same for all phases.

ZS :secondary leakage impedance, or the part of Z caused by the transformer secondary windings only, assumed the same for all phases.

Zx =the exciting impedance, or mutual impedance between primary and secondary windings of each phase of transformer 3, assumed the same for all phases.

As the neutral point of the star-connected winding 4 is ungrounded, the high-voltage circuit l is three-phase three-wire, and the total power flow therein may be measured as the sum of the conjugate products of the currents in any two phase conductors and the corresponding voltages of the two conductors with reference to the remaining conductor. Taking the b-phase conductor as reference, the total power flow is P where Neglecting exciting current in the transformer 3, the primary voltages are equal to the sum of the secondary voltages and the corresponding leakage impedance drops:

Eu '=Ea+[a' 'Z Eb"=Eb+Ib"Z (2) Ec"=Ec+Ic"Z Because of the star-delta voltage relationship at the primary windings 4 of transformer 3 (see Fig. 2) the voltages Ea and E0 may be represented as Ea'=Ec"Eb"}' (3) E '=E E Substituting (2) in (3) The Equations (4) express the high-voltage quantities Ea and Ec' in terms of three voltages Ea, Eb and E0 of the low-voltage circuit 2, and the three delta currents I a, I"b and I"c circulating in the secondary windings 5. As the delta currents cannot be conveniently measured without special connections, it is preferable to substitute the secondary phase currents for the delta currents. Also, as the circuit 2 is three-phase, three wire, one secondary current and one secordary voltage may be eliminated from Equations (4:).

The relationship of currents at the junctions of the delta is The relationship of voltages at the de1ta-connected windings 5 is, as shown vectorially in Fig. 2,

Eb=-Ea-'Ec (6) Substituting (5) and (6) in (4) and rearranging Equations ('7) show that the phase-to-phase voltages of circuit i may be expressed as functions of two secondary phase-to-phase voltages and a secondary phase current of circuit 2. However, as there is a circuit around the delta which could carry a residual or zero-sequence current component, the polyphase quantities of circuit 2 can be completely expressed by these variables only if the flow of zero-sequence current is prevented. It is therefore necessary to establish that no zero sequence current circulates in the delta for the above relationships to hold rigidly.

It will be noted that the terms IaZ and IBZ of Equations (7) above are each derived from a plurality of terms of Equations (4) and appear as single terms in (7) only because the same value of leakage impedance Z has been assumed for all phases. As the terms IaZ and ICZ represent compensating voltages introduced by the compensators l3, it will be apparent that symmetrical leakage impedances Z of the power transformer 3 are necessary for accurate compensation in accordance with the principle of the invention.

The voltages acting around the delta consist entirely of mutual impedance drops derived from the primary phase currents, and the self-impedance drops of delta currents in the secondary leakage impedances Z. The voltage equation the delta, accordingly, is

However as the high-voltage circuit I is assumed three-phase, three wire,

I'..'+Ib'+1c'=o (9) Substituting (9) in (8) and factoring I"+Ib"+Ic"=0 (10) As the delta currents add to zero, there is no circulating current in the delta which could disturb the relationships stated above. It will be noted that Equation (8) holds only if the exciting impedance Zx is symmetrical in all phases and the secondary leakage impedance Z. is similarly symmetrical. It may also be shown that symmetrical primary leakage impedance of the transformer 3 is necessary to eliminate any residual component of the primary star voltages with reference to the junction point of primary windings 4, in order to provide power measurements rigidly following Equation (1).

Fig. 3 shows a modified potential transformer arrangement which may be substituted for the potential transformers ii of Fig. 1. In Fig. 3 the potential transformers 25 are provided with two secondary windings" and 21,0ne having twice the number of turns of the other. By proper connection of the windings 26 and 21, the two output potential circuits may be separately grounded, as may be desirable for energizing star-connected measuring devices or for other reasons.

Fig. 4 shows an alternative construction of impedance drop compensator which may be substituted for the compensators ii of Fig. 1. In

- the Fig. 4 construction, a parallel connection of the reactance section 3| and the resistor 32 is employed, eliminating the necessity for an auxiliary potential transformer, such as the transformer II of Fig. 1. l

I do not intend that the present invention shall be restricted to the specific structural details, arrangement of parts or circuit connections herein set forth, as various modifications thereof may be eflected without departing from the spirit and scope of my invention. I desire, therefore, that only such limitations shall be imposed as are indicated in the appended claims.

I claim as my invention:

1. In an alternating-current system, apair of polyphase circuits, translating means including a closed circuit connected to all phases of a first of said polyphase circuits' and having substantial- 1y uniform leakage impedance between all phases thereof, said closed circuit having substantially uniform mutual impedance to all phases of the second of said polyphase circuits, and means for deriving voltages of one of said polyphase circuits from the other thereof comprising phaseshifting means for correcting the shift of phase voltages in said translating means, and compensating means for correcting the leakage impedance voltage loss in said translating means.

' 2. In an alternating-current system, a pair of three-phase. circuits, translating meam including three-phase three-wire circuits,

a delta circuit connected to all phases of a first of said three-phase circuits and having substantially uniform leakage impedance between all phases thereof, said delta circuit having substantially uniform mutual impedance to all phases of the second of said three-phase circuits, andmeans for deriving phase voltages of one of said threephase circuits from the other thereof comprising means for combining components of delta volt-- nected to said low-voltage circuits and star-con- I nected windings connected to said high-voltage circuit, said transformer means having substantially uniform leakage impedance in said deltaconnected windings, substantially uniform leakage impedance in said star-connected'windings and substantially uniform exciting impedance in all phases, and means for deriving voltages of said high-voltage circuit from said low-voltage circuit comprising means for dividing two delta voltages of said low-voltage circuit in equal components and for adding said components to undivided delta voltages in such manner as to substantially duplicate the phase voltages of said high-voltage circuit as to phase position, and compensating means for correcting the leakage impedance voltage loss in said translating means.

4. In an alternating-current system, a pair of three-phase three-wire circuits, transformer means having star-connected windings connected to one of said circuits and delta-connected windings connected to the other of said circuits, said transformer means having constants such as to substantially exclude the circulation of zero sequence current in said delta-connected windings, and means for deriving voltages of one of said three-phase circuits from the other of said circuits including compensating impedances and means for energizing said compensating impedances in accordance with current quantities derived from the phase currents of said other of said circuits.

5. In an alternating-current system, a pair of transformer means having star-connected windings connected to one of said circuits and delta-connected windings connected to the other of said circuits, said transformer means having constants such as to substantially exclude the circulation of zero sequence current in said delta-connected windings,

EDWIN L. HARDER.

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