US2546021A - Control system - Google Patents

Description

March 20, 1951 w. K. SONNEMANN 2,546,021

' CONTROL SYSTEM Filed April 50, 1945 P? J k a I'LI'LI'L%J'L on I I H 4 Id 1 5 I o P j o I b C A; 2

WITNESSES! INVENTOR Wz'ZZz'a m/f. 50777767776177.

ATTORN EY Patented Mar. 20, .1951

ssignor.to--Westinghouse Electric Corporation, jEast Pittsbui-gh la a corporation or Pennsyll'vania' ApplicationApi-il 30, 194 5,' Serial No. 591,9 ?9 7' e rns. (c n-. 119) '1 3 My present invention relates to phase-sequence filter-networks, for; selectively responding to dif ferent phase-sequence components of-a threephase line-current or dine-voltage, and' to ,control-systems utilizing such j f lters.

My invention is an improvement ..upon the present. knowledge of the art, with respect tosequence-filters, as represented in the sequencefilterdiagrams and explanations given on pages 248 and 249 of the El ectrical Transmission and ,Distribution ReferenceBook, 1942 :edition, published by WestinghouseElectric .& Manufacturing Company.

.An object of myeinvention is accomplished by providing a sequenc'eefilterwhichwill respond to both the positive and negativephase-sequence componentaand more specifically, a filter which responds strongly. to the negativeesequence components of the impressed three-phase current or voltage, and only in-.a small degree to the positive-sequence component, or .to jthe combined positive and zero-sequence components.

This large"disproportionality of the responses to the positive 'andnegativ'e-sequence ..comp'o- 'nents is particularly important whenltheffilter. is

utilized in a "control-system ,for obtaining a relaying-response to different kinds. of ffaultson a transmission-line, in response tofdiifer'eiit phasesequence components ol the} three-phase linecurrent. I Heretofore; the mostisuccessful relaycontrol scheme; for responding,in-one unit, to

any of j'the differeritfkinds of faults which, are possible on athree-phasejline, has-been the type HCB orHKB system,""u'tilizing a filter having 249 of the. above menjtio'nedreferencebook.

' In spite ofithree major difliculties or shortcomings, the positive-plus-zero filterhas enjoyed a longand widespread use, since" its inception.

One of its difficultieshas be'en:that the relative phase-positions of the positive and zero-sequence components of thelfne-current have been difierent,*'foi' 'faults ozr different phases, 'so* that the absolute magnitude .of the vectorial1 sum of these *twocomp onents has been'jsubjectj to jvariation, according tojwhichph'ase was, faulted, even consideringfaults'whichare of" the same type,

such as 'single -phase" ground-faults, *phasetophase faults,*and' doublephas'e-to-ground"faiilts. An'oth'e'r "difiic'ulty has'been its "response to positive'sequence" currents; necessitating a relay-setting higherthan the full-load current ofthe line, "frequently resuitingin irisufiicient'sehsltivityto single-phase-ordouble-phase ground -faults, particularly-in cases where the'zer'o-sequence- 'cur- -'-rents were' relatively-small; "Another possible "objection to the positive-pluszero sequence filter has been anobjetiom whieh v:=is at. least a.theoretical possibility, that-it iss'poszsiblefor the relay toha-ve nowresponseat-allnto certain :phase-BC ground-faults in iwhich-.; the positive-sequence component and. the weighted zero-sequence component might .happeneto be nearly equal and opposite. in phase,1s'o as to. canjeeitut ea'ehother, in some articuiartran'smisi Ihese'difficulties are now avoided, in my pres- .ent' 'inventiomb'y. combining the positive and begative-sequ'ence 'r'esponses'in' as'ingl'e filter, "and by heavily weighting .the negative-sequence response, as by making it, say, eight or nine times more sensitive than the positive sequenceresponse, so that a relay which is conneetedto'the output-termina ls-lof the-filtenwillrespond substantially only to the negative-sequence m-agni- "tilde; for all kinds offaults where there is '"any negative sequence warrant-component, and yet which will respond to balanced three-phase faults, which have only"tliepbsitive-sequence current-component. Since .threeephasewf'aults are nearly always .very severe faults, a fault- "rsponsive relay does'notfin general, need to have any great sensitivity in order to respond to such faults, whereas, -forcertain other types of faults, the fault curren'ts may be considerably smaller than :the' full load line curr'ent; as is well known, so thatma considerable relayesensitivityeis required. ;-An advantage or havingthe-rela-y-volt- 'age composed of-eightor ninetparts. negativesequenceflresponse, and one part @pesi-tive-sequence response, isthat' the vectorial sum of these two responses-"does 'not *charige" too much in dependenceupon-the relat-i-ve phase of the positive-sequence component with respect to, the negative-sequence component, according to which line-phase, or phases, are faulted, because the positive-sequencer component is such'a small "percentage of the large negative-sequence component of the relay voltage.

"Heretofore, ajdouble response tothepositive and negative phase-sequence components of the line-current, heavily weighted in {favor of the negative-sequence ..response, and excluding the "zero' sequence response, has been impractical be cause of' the necessity for utilizing two separate phase-sequence networks, one responding to the positive-sequence current and the other responding to the negative-sequence current.

With the foregoing and other objects in view, my invention consists in the circuits, combinations, systems, apparatus, elements and methods hereinafter described and claimed and illustrated in the accompanying drawings, wherein:

Figure l is a diagrammatic view of an embodiment of my invention in the form of a sequencefilter for developing a single-phase outputvoltage,

Figs. 2 and 3 are vector diagrams illustrating its response to positive-sequence inputs and negative-sequence inputs, respectively, and

Fig. 4 is a view similar to Fig. 1, showing how a zero-sequence response may be added, if desired.

In a positive-sequence system of vectors, Ia, b Ia and I=Iae the differencecurrent (jbc) l.732.zae In the negativesequence system, Ia, I'z1=Iae and Ic=Iae the difference-current (iii-Io) =l.'132Iae leading Ia instead or lagging behind Ia.

In a negative-sequence nlter, having a singlephase output-voltage as snown in the henenan Patent 2,161,629, granted .June 13, 1939, imp ed ances Z9. and Zb are used, traversed respectively by It. and. (it-Iv); and the no-load or open-circuit output-voltage of the network is equal to the dmerence between the voltage-drops IaZa and (i'bic)Zb in the two impedances Za and Zb. Since the network is to respond only to negative-sequence currents, its no-load outputvoltage must be zero when positive-sequence currents are supplied to the network. This means that the magnitudes and. relative impedancephases of the impedances Z8 and Z1; are such that v 1az'a=(ib-ic)zb (1) for 'positivesequence currents. Putting z'a=z..e and Zb=zbe 2) and substituting 1.732Iue =;i1.732Ia for lit -f), Equation 1 states, in effect, that iazae =1.732Iazbe (3) which means that Zb=.577Za (4) and.

In a usual case, as shown in the Lenehan Patent 2,161,829, Z3, is a pure resistance, meaning that the impedance-angle (2:0, and hence, from Equation 5, the other impedance-angle b=90, thus defining Zb as a pure inductive reactance such as a mutual reactance In accordance with my invention, I proportion the filter-impedances of a negative-sequence filter so that Equations 1 and 3 do not hold true, either because the two voltage-drops IaZae and 1.732IaZte are not in phase with each other, or are .of different magnitudes, or both. The output-voltage Er of the phase-sequence network of said Lenehan Patent 2,161,829 is the difference between the two voltage-drops 12.22. and (lir -i025, so that, if said voltage-drops are equal,,as on positive-sequence energization, the output-voltage Er is zero, whereas, on negative- 4 sequence energization, the second voltage-drop reverses, so that the output-voltage is More specifically, it is an important feature of my present invention to make the difference between the two voltage-drops [IaZa- (fbI'c) Z21] have a magnitude, such as one-eighth, or oneninth, or other fraction, preferably a small fraction, of the magnitude of the sum of these voltage-drops, [RZa-l-(ib-idZb]. The effect of this design-arrangement is to make the filter predominantly a negative-sequence filter, so that the magnitude of its output-voltage is not greatly affected by the phase of the relatively small positive-sequence component, and yet providing a relay which is capable of responding to balanced three-phase faults, for example, which have no negative-sequence component. At the same time, the negative-sequence response enables the relay to remain unresponsive to the balanced threephase load-currents of the line, because the line current has no negative-sequence component, except when there is an unbalanced fault on the line, such as a single-phase fault, or a two-phase. fault.

It is to be understood, of course, that my invention is of general application to negativeseouence filters of all descriptions, the basic general idea of my invention being to design the negative-sequence filter so that its output-voltage is not zero, when the filter is impressed with positive sequence currents or voltages. More specifically, an important feature of my invention is to so choose the filter-constants, that is, the impedance-magnitudes and impedance phaseangles of the various filter-impedances, so that the filter-output, on positive-sequence energization, has a magnitude equal to one-eighth, or one-ninth, or other small fraction, say between one-fourth and one-twelfth, of the magnitude of the filter-output when impressed with a negativesequence input of the same magnitude as the positive-sequence input.

These general principles of my invention are applicable to any of the sequence-filters which are shown on pages 248 and 249 of the abovementioned reference book, or to any other sequence-filter which can be devised, the basic principle being to make the filter-output, as a result of positive-sequence energization, not zero, but a certain small fraction of the filter-output as a result of negative-sequence energization. The methods of calculation of the filter-performance, in terms of the various filter-impedances, are Well understood, and are explained, for example, in the reference book citation;

In the illustrative filter-network shown in Fig. 1, the filter output-voltage Er is equal to the difference of the voltage-drops as follows,

where Ra is a resistance, traversed by the phase-A input-current Ia, said resistance being connected between the input-terminal m and the output-terminal n of the network. The outputterminal n is also the star-point connection for the three-phase input-currents la, is and ic. The mutual reactance M is the reactance between the winding I and each of the windings 2 and 3 of a mutual-reactance device I, 2, 3, having the windings 2 and 3 traversed, respectively, by

resistor-tap 4 is at the two-thirds pointin'the resistor Ra, it is evident that Vmn=Ia('%'Ra) (1 b+jc) /gRa) (8) If we designate the positive, negative, and zero phase-sequence components as In, 1&2 .andin, re-

.spectively, then it follows,.from the definitions of symmetrical coordinates, ."that n al'+ a2+ b 111 h zardn c al+ a2 Substituting these Values. in Equation, 8,

thus eliminating the response to the zerosequence componentio. But

1+a+a ==O (11) and hence Equation shows that the two-thirds tappoint 4 on the resistor Ra eliminates the networkresponse to the zero-sequence curent'Io.

The result which is shown in Equation 13 could have been arrived 'atin another way from the equation I0=%(Ia+jb+ c) (14) from which it will be seen that, in a system in which the zero-sequencecurrent I0 is either zero, or can be ignored, or regarded as :being zero, because of Equation 10, then Ia=-(ib+ic) 15) and Equation 8 instantly becomes Vm1L=IaRa (16) in a system in which the zero-sequence currents are absent or inefiective.

In the pure negative-sequence network, the value of the mutual reactance M is equal to .577Ra, sothat'Equations 1 and 3 are satisfied. In accordance with my invention, the ratio of the mutual impedance M to the resistance Rs. isnot .577, but some other quantity, either real 'or imaginary, that is, either with or without a phaseangle. In particular embodiment of my invention shown in Fig. 1 and analyzed in Figs. 2 and 3, the ratio M/Ra=.8 .577, or .462, so that the output-voltage E z-=Vpn+, for positive-sequence inputs of a given magnitude," isone-ninth of the output voltage Erwn for a negative-sequence input of the same magnitude asthe positive-sequence input. In other words, the mutual coupling between the windings l and 2, and between the windings I and 3, is 7'0.462Ra, as indicated in Fig. 1.

In Fig. 2, it is assumed that the input-currents 6 Ia, ib and 10 have the positive-phase-sequence, so that the difference-current ('Ib'Ic)'lags90 behind Is, as shown. The voltage-drop Vmn=RaIa is shownin Fig. 2 in phase'with'the phase-A current Ia. The voltage drop 0.462 X 1.732Rala=0.8Rala as shown in Fig. 2; this voltage-drop being fourfifths as large as'thevoltage-drop Vmn because the value of the mutual impedance isAGZRa instead of the value .577Ra which it would have in a pure negative-sequence network. This voltage- 'drop -V leads the difference-cu'rrlent vector (ID-Io) by so that it is in phase with the Voltage-drop Vmn. Theterminal output-voltageof the sequencerfilter or network is equal to (V -Vq whichis shown at V the. plus sign,

fin the subscript, indicating that it is the outputvoltage for a positive-sequence current-input.

Fig. 3 shows the vector-conditions for'thej same 'magnitude of input-'curents, but with the inputcurrents -Ia, I b, I ahavingthe negative phasesequence, so that-the difference-current (lb-1c) leadsthe phase-Acurrent It. The mutual-reactance voltage-drop Vqp leads the differencecurrent vector (Ib-1c) by 90, as before putting the reactance-voltage-drop Vq in phase o'pposition to the resistancevoltage-dropvmn, so that the output-voltage Vpn, which is equal to (Vmn-Vqp) or (Vmn-I-Vqp) is numerically equal to the 'sum'of the magnitudes'of the two 'volt'agedrops, instead ofbeing equal to theirfldiffer'e'nce as in Fig. 2.

It is to be understood, of course, that an infinite number of other proportions are possible, the parti'cular proportions which are illustrated in Figs. 1, 2 and 3 being intended-merely as illustrative.

The total output-voltage ET V of the network, when the impressed currents Ia-Ib and I6 have both positive and negative-'sequence-components, is equal. tothe vector. sum of the filterresponses to. the individual sequence-components of the input-currents. 'Theze'rd-sequence components of the input-currents have no effect upon the network shown in Fig. 1', because. of the -point connection for the residual current 310. In the particular filter shown in'Figs. 1, 2:and 3, these two'output voltage componentsV n and Vpn, torv positive and negative-sequence inputs,

respectively, are in phase with each otheryronly ifthe positive and-negativep-sequence input-componentsIn and-IE2 are in phasewitheach other. .Whatever the relative phase between these two filter-voltage components, V n and Vpn-, the resultant output-voltage is thevectorial sum of the two.

An advantage of my invention is'that one of these components, vpn+, is quite small compared with the other component,-V n ,in all cases except when the negative-sequence input c'urrent componentlaz is quite small with respect to the positive-sequence input-current component In. Most relaying equipments (not shownl'which .may be connected to the output-terminals p and .n of.-the filter-network, are either responsiveito themagnitudes of the total or-resultant filterresponse Er to both phase-sequences, orthey are at least affected, in some way, by the phase and magnitude of the resultant filterevoltage, so that it is desirablefor the magnitude of 'the resultant filter-voltage to be fairly constant, for faults occurringondifferent ones or combinations of the three line-current phases A, B and C.

Table (for Fig. 1)

I II III IV V VI VII VIII IX Fault In In! 4 pn+ pn- V I 5 Degrees A-B-C 5 None 0 5 5 1. 0 AB 2. 88 2. 88 60 2. 88 25.92 27. 5 0.91 5. 5 BO 2. 88 2. 88 180 2. 88 25. 92 23. 0 l. 09 4. 6 CA 2. 88 2. 88 +60 2. 88 25.92 27. 5 0. 91 5. 5 A-G 1. 67 1. 67 0 1. 67 15. 03 16. 7 l. 5 3. 3 B-G 1. 67 1. 67 l2() 1. 67 15. O3 14. 3 1. 75 2. 9 CG 1.67 1.67 +120 1.67 15.03 14. 3 1. 75 2. 9

The operation of the filter-network shown in Fig. 1 is indicated in Table 1, for different types of faults, such as a three-phase fault A-BC, a phase-to-phase fault AB, BC, or CA, or a lineto-ground fault A-G, BG, or C-G. Columns II and III indicate, respectively, the positive and negative-sequence current-components In and I212, when the actual fault-current is 5 amperes. Column IV indicates the phase-angle I of the positive-sequence component In with respect to the negative-sequence component 19.2 for the type of fault in question. Columns V and VI indicate the filter-voltage components Vpn+ and Vpn for the phase-sequence input-currents Ial and IaZ, respectively, based on the particular design-constant, M =.462Ra, which has been described. Column VII indicates the magnitude or absolute value of the total filter output-voltage V, which is the vector sum of the components vpn+ and vpn-, with the phase-angle 6 between them. Column VIII indicates the line-amperes I which would be necessary to produce a filter-output voltage V of 5 volts. Column IX indicates the relative sensitivity S of the network-response to the various types of fault, taking the threephase fault as a basis of comparison.

It will be seen, from the table, that the network of Fig. 1 is more sensitive to the unbalanced phase-to-phase faults AB, BC, CA, and to the single-phase ground-faults AG, 13-6, CG, than to three-phase faults AB-C, which is precisely what is desired, because the actual fault-currents which flow in the line-conductors, of a. transmission-line, for example, have a tendency to be larger for three-phase faults than for single-phase faults.

The sensitivity for two-phase-to-ground faults has not been shown in the table. This is because the proportion of the negative-sequence current-strength 12.2 to the positive-sequence current-strength In, for such faults, depends upon the impedance of the zero-sequence network of the transmission-system under consideration, whereas, for all other types of faults, the positive and negative-sequence current-components IE1 and 1&2 are equal, except in the case of the balanced three-phase fault, which has no negativesequence component. Considering the conditions during a double ground fault, it is usually true that the zero-sequence impedance of the line is large, in proportion to the positive and negativesequence impedances, which are about equal to each other, so that the sensitivity of my sequencenetwork to double ground faults would be somewhere intermediate between the values shown for the single ground faults and the ungrounded phase-faults, approaching the sensitivity for the phase-fault condition. In transmission systems where the zero-sequence impedance is quite low, the sensitivity of the filter-network of Fig. 1, to two-phase-to-ground faults, would approach that of the three-phase fault-condition. Again,

Ill

the operation of my filter-network is quite satisfactory.

Another important condition to be noted, in connection with the operation of the filter-network of Fig. 1, as shown in the table, is the relative insensitivity as to which phase is faulted, in the event of a fault involving less than all of the phase-conductors of the line. This is really a very advantageous condition, which has been a serious shortcoming of most previous networks for producing a single relaying voltage which is r intended to be responsive to all different kinds of faults. This is accomplished by making the positive-sequence response small, as compared with the negative-sequence response, so that the unavoidable variations in the phase-angles between the positive and negative-sequence components will not make too much of a change in the magnitude of the total response, while, at the same time, having some positive-sequence response, so that the filter-system can respond insensitively to balanced three-phase faults.

Fig. 4 shows how any desired amount of zerosequence response may be added to the response of Fig. 1, by adding a zero-sequence resistor R0, or, in general, any zero-sequence impedance Z0, connected between the star-point n of the inputcurrents Ia, Ib, I and the network output-terminal n, with the 310 return-circuit connected to any desired point 4', tapped off from the resistance R0. This change in the connections adds any amount of zero-sequence response, in the manner set forth in the previously mentioned Harder Patent 2,183,646, or in the network (q) of the reference book citation.

In operation, the network shown in Fig. 4 makes it possible to increase the sensitivity to ground faults, such as the faults A-G, B-G and C-G of the table. An important feature of the old type-HCB or HKB network, having only positive-sequence and zero-sequence responses, was its high ground-fault sensitivity, which was usually 8 times as great as its sensitivity to threephase faults. In the first form of my new network, as shown in Fig. 1 and the table, using positive and negative-sequence responses, but no zero-sequence response, the ground-fault sensitivity was only about 3 times as great as its threephase sensitivity, and if an attempt were made to increase the ground-fault sensitivity up to 8 times the three-phase sensitivity (by greatly decreasing the positive-sequence response, relatively to the negative-sequence response), then still higher phase-fault sensitivities would be obtained, which might cause trouble because of normally slightly unbalanced phase-to-phase loading, or because of other line-conditions.

The addition of the zero-sequence response, in Fig. 4, in addition to the positive-sequence and negative-sequence responses of Fig. 1, makes it possible to obtain any desired relative sensitivity to single ground-faults, while at the same time using ratios considerably smaller than 8-to-1 or 9 -t-1, for the ratioof negative-sequence topositive-sequence response, thus making the phasefault sensitivity approach more closely toward the three-phase sensitivity. For example, if the three-phase sensitivity is again taken as unity, as in the last column of the table; itis possible", in Fig. 4, to obtaina sensitivity ofi1l2 forABand CA faults, and: 1.9 for BC-faults,-while different tap-settings onth ezero-sequenc e resistor R0 provide ground-fault sensitivities of 4, or 8, or any other desired-value, with onlyslight variations depending upon which phase is faulted. This is only an illustration.

At the same time, the presence of responses to all three of the phase-sequence components, in Fig. 4, enormously reduces the possibility or likelihood of all three components so nearly neutralizing each other as to have any difficulty in responding to BC double ground faults, as has sometimes been suspected in the case of the older type-HOB or HKB network.

By providing a tap 5 on the reactance-winding 1 in Fig. 4, it is readily possible to change the ratio of negative-sequence to positive-sequence response, making this ratio have any of several available values corresponding to the number of tap-positions provided. At the same time, the amount of zero-sequence response can be adjusted by means of the tap 4' on the zerosequence resistor R0; or the zero-sequence response can be cut out entirely by using the onethird-point tap 4 on the phase-A resistor Ra, as in Fig. l. The embodiment of my invention, shown in Fig. 4, is thus quit versatile.

A network such as shown in Fig. 4 might also be necessitated for some special application, such as detecting a two-phase-to-ground fault on the star side of a delta-star transformer-bank at the far end of a long transmission-line (not shown). In such a case, the impedance of the equivalent zero-sequence network of the transmission system will be relatively low, meaning that the zerosequence current-component will be large, while the negative sequence current-component will be very small, and the postulated long length of the transmission-line means that the fault-current will necessarily be small. Because of the smallness of the negative-sequence component, the response of my Fig. l filter to such a fault will approach the sensitivity for three-phase faults, which is not very great, because of the smallness of my positive-sequence response; and in the case of a long line, this degree of sensitivity to the positive-sequence current-components probably would not be adequate, without the addition of the zero-sequence response, such as is obtainable in Fig. 4.

While I have illustrated my invention in two difierent forms of embodiment, I desire it to be understood that such illustration is only illustrative, and by no means limiting, as to the applicability of my invention to different types of networks. Some of the general principles of construction and application have been set forth in the foregoing description, and other applications of the principles of my invention will be obvious from the description which I have given. I desire, therefore, that the appended claims shall be accorded the broadest construction consistent with their language.

I claim as my invention:

1. A phase-sequence-current filter-network for selectively responding to a plurality of phase-sequence components of an impressed three-phase current, said filter-network comprising, in-effect,- two-impedances, Za=Zae -andZb Zz5e circuitconnections for causing the impedance Za to be;

traversed, in efiect', by any one of the phases of the impressed current, and for causing the im-' pedance Zb to be impressed, in effect, by the di f characterised by the impedance Zae having a vector value' substantially different from 2. A phase-sequence-current filter-network having a resistor, a three-winding mutual reactance device, input-terminals for an impressed three-phase current, output-terminals for a single-phase output-voltage, circuit-connections for energizing said resistor and two of the windings of said mutual reactance device in star-circuit connection from the several phases of the impressed current, and circuit-connections for energizing said output-terminals from a circuit serially including said resistor and the third winding of said mutual reactance device, characterized by said mutual reactance having a value substantially different from .577 times the value of the resistance.

3. The invention as defined in claim 2, in combination with a return-point tap-connection on said resistance at a point one-third of the resistance, measured from the star-point, for cancelling out the zero-sequence response.

4. The invention as defined in claim 2, in combination with a zero-sequence impedance traversed by the zero-sequence current flowing from said star-point, the output-circuit connections including said zero-sequence impedance.

5. A negative-plus-zero phase-sequence current-segregating filter-network for selectively responding to a desirably weighted vectorial sum of the negative and zero phase-sequence components of an impressed three-phase current, said filter-network comprising a plurality of impedances, in different phases, with the impedances so proportioned that the output-voltage of the filter-network has a relatively large value when the impressed three-phase current has no phasesequence components other than the negative phase-sequence, and so proportioned that the output-voltage of the filter-network has a relatively small, but substantial, value when the impressed three-phase current has no phase-sequence components other than the zero phasesequence, and so proportioned that the outputvoltage of the filter-network has a relatively small, but substantial, value when the impressed three-phase current has no phase-sequence components other than the positive phase-sequence.

6. A phase-sequence-current filter-network for selectively responding to a plurality of phasesequence components of an impressed three-phase current, said filter-network comprising, in effect, three impedances, Z'a=Zae Z'b=Zbe and Z0, circuit-connections for causing the impedance Za to be traversed, in effect, by any one of the phases of the impressed current, and for causing the impedance Zb to be impressed, in effect, by the difference between the other two phases of the impressed current, and for causing the impedance Z0 to be traversed by the zero-sequence current, and circuit-connections in effect serially 11' connecting said impedances for producing an output-voltage responsive to the vectorial sum of the three voltage-drops thus produced, characterized by the impedance Z16 having a vector-value substantially difierent from 1.732Zbe 7. The invention as defined in claim 1, characterized by the magnitude of the vector-difierence between IaZae and 1.732IaZbe being relatively small as compared to the magnitude of the vector-difierence between Itzae 1.732IaZbe for any value of the impressed phase-A current Ia.

WILLIAM K. SONNEMANN.

and 10 REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 1,567,581 Evans Dec. 29, 1925 1,963,193 Evans June 19, 1934 FOREIGN PATENTS Number Country Date 483,729 Great Britain Apr. 21, 1938

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