US2495158A - Phase shifter - Google Patents

Description

Jan. 17, 1950 H. J. CARLIN 2,495,158

PHASE SHIFTER Filed March 21, 1945 WITNESSES: INVENTOR 4??- herberfJCafl/h.

547711 72, A M I W ATTORNEY Passes an. 11,1950

' usrrso' STATES PATENT OFFICE rnass smrrsa Herbert J. Carlin, East Orange, N. 1., assignor to Westinghouse Electric Corporation, East Pittsburgh, Pa., a corporation oi Pennsylvania Application than 21, ms, Serial No. seam 1 My invention relates tophase shitting-networks, and it has particular relation to a simple 14 Claims. (01.323-120) and convenient network ior shifting the relative Number 2,393,983, granted February-5, 1948; A

significant feature '01 this Goldsborough relay was the application 01' two voltage-components to a relay-coil, which was the restraint-coil 01' a baltransformer 4, which supplies the current ii to an adjustable compensator-impedance Z1=Ri+1li I My invention has particular referenc to the phase-shitting network i, having output-termianced beam impedance-relay, the two voltagecomponents being responsive, respectively, to the line-current and the line-voltage, with means for varying the magnitude '0! the current-response, and means for varyingthe relative phase-angle between the two responses. The phase-shitting means was included in the voltage-responsive 4 energizing-means, in accordance with my present invention. a

The object of my invention is to provide a simple and versatile phase-shitting network for accomplisliing the purpose just stated.

The accompanying drawing consists of a some what simplified and idealized diagrammatic view .of circuits and apparatus my invention.

As shown in the drawing. a load-device Z, such as a relay-coil, is supplied with an alternating relaying-current iz which is supplied from a voltage-responsive source E and frame current-re sponsive source KlZl, which is shown asbeing connected in opposition to the voltage-responsive source, although it could be connected in either polarity. The line-voltage E is applied to the input-terminals Ti and T2 of a network I according to my inventiomirom an alternating-current line 2. Another alternatingcurrentsource K'iZl oi the same frequency as the voltage-source E, but ot a varying phase-relationship, is provided, and for convenience or reference and illustration, I shall refer to it and illustrate it as a current-responsive source, although it might be another voltage-responsive source. so far as my present invention is concerned. The current-responsive source K121 is represented as receiving energy from the line I through a line-current tramiormer I, which supplies the line-current i to a variable auxiliary variable resistor R1.

nals TI, T2, in addition to the input-terminals TI, T2, The load 2 and the adjustable compensator-impedance 21 are serially connected across the output-terminals T3 and T2. The network i comprises a phase-shifting transformer T and a The transformer T has a primary winding 1x1 having m turns, and a secondary winding 1X2 having m=nm turns.' The primary winding-1X1 and the variable resistor R1 are connected in series with each other across the input-terminals TI and T2. The secondary winding 1X: is connected between the terminals TI and T3. The resistance oi'the primary winding iXi may be conveniently regarded as being "included in the variable resistance R1, and the resistance ofthe seco winding 1X: is regarded as being included in the load-resistance R oi the load impedance Z=R+!X.

By Thevinin's theorem, the relaying current is is given by the equation where l lw=the no-load output-voltage of the voltageresponsivenetwork I, with no load connected to its output terminals T3 and T2,

Eio=the no-load current-responsive voltage film, without any connection to the load-device Z,

and. I v

Z=the total impedance, with all voltage-sources short-circuited.

From the drawing, it is evident that the induced secondary voltage due to the primary current 11 of the phase-shifting transformer T is ia=i ll 1 1' XiI 1 (2) since the mutual reactance, neglecting leakage. I

The primary current 11 of the unloaded phaseshii'ting transformer T is obtained by dividing the impressed voltage E by the primary-circuit impedance, which is Therefore. the no-load outwit-voltage of the voltage-responsive network is sin from Equation 4. and remembering that1=e Remembering that e -col 9+! sin 9, we may rewrite Equation 5 as B,.-=AEe '=E[l-n sin p.(sin p+j cos p)] =E(l-n sin p-jn sin p cos p) (6) since cos 2p==i-2sin'p,and sin2p=2sin p cos p, and rm=cos 29-1 sin 29.

The values of A and a are determinable from Equation '1, from which it is apparent that -.J1+%(n -2)(1- 2p) Equation 7 also shows that:

M "1?) Puttin:

and

'z x n (12) we may write the no-load current-responsive voltage as as=itizi=irum+ (13) Putting Z=lse" and Z'=Zre" wemaywritethetotalimpedancelsas z X X, l l +ZYQI' and the current-responsive current-component Ens/2s, it does not affect the relative phasetor Zs in Equation 1 does aii'ect the magnitude of the total relaying-current iz, and hence it is necessary to examine the constancy of the absolute magnitudes of the right-hand side oi Equation 16. The total impedance is is the vector sum 01' three vectors, X: cos p 6 Zac and Zrc. It is quite feasible, and desirable, to make the secondary-winding reactance K2, and the relay-impedance Zz very much greater than the compensator-impedance Z! of the current-responsive source KiZ1, so that the compensator vector-component Z12 is swamped." This compensator-impedance Zre is subiect to variation, when Z1 is varied for the purpose oi varying the amount or the current-responsive voltage KZL which is applied to the relay Z, but since it is only a very small part of the total impedance is, the resultant variation in is is small enough to be neglected.

Neglecting Z:=Zrc", therefore, Equation 16 reduces to tion in Equation 1, showing the relaying current to be where A, a and Zs have the values shown in Equations 9, 10, 18 and 19. The phase-angle between the voltage-responsive voltage-component AEe" and the current-responsive voltagevcomponent KIe is (o-i-k-a), where the efiective phase-shift angle a of my phase-shifting network I is as shown in Equation 10.

Considering the magnitude 0! the voltageresponslve relay-current component AEe /zs, it will be noted that the magnitude-coemcient of this quantity is expressed by the fraction A/Zs. Neither the numerator A nor the denominator Zs remains absolutely constant as the primarycircuit impedance-angle p is varied by varying the adjustable resistor R1, but the departures from constancy are small enough to be within the permissible percentage-error oi the relayresponse, and the two' errors at least partially oilset each other, in the line-voltage response, although the error in the constancy oi. the common denominator Zs is not compensated in the line-current response KIe /Zs.

The denominator Zs is shown, by Equation 18, to be the resultant of three component vectors, represented by the three terms at the right-hand side of the equation. As previously explained, the third term is small enough, with respect to the other two terms, so that its effect on the constancy of the resultant impedance-vector may be neglected, or an average value of the third term maybe included, if desired. as a of the voltage-responsive component AEc VZsof the relaying current is in Equation 20. Equation 9 shows that the variation in the quantity A can be calculated diagrammatically, utilizing the vectors Just discussed, for different values of p, or it may be calculated from either one of equations 18 or 19. For reasonably small values of the primary-circuit angle p, and for values of the relay-impedance Zz, which are at least approximately commensurate with the secondarycircuit inductance X: of the phase-shifting transformer T, the value of Zs increases by only a small percentage; when p is changed from 0 to 26, for example.

The variation in the magnitude Zs will be the least, or substantially least, when its value at p=o equals its value at p=P, as p varies between the limits 12:0 and p -P. Making this calculation from Equation 19, we find the value of the load-reactance X. in terms of the loadresistance R, the secondary reactance xx, and the maximum value P of the primary-circuit impedance-angle p, as follows:

Thus, if p varied between 0 and 26, the loaddevice Z would preferably have a reactance x p=0, tan p-%=zero which is to saythat the primary resistance In is infinitely large, or open-circuited. If

which is to say that the variable primary resistance has been reduced to a value equal to 1.732 times the inductive reactance Xi of the transformer T. In other words, the primary resistance Ri is very large compared to the primary inductive reactance Xi, and greater than 1.7Xi.

In an actual embodiment of my invention, which is mentioned only for purposes of illustration, R. was 3800 ohms, X: was 4550 ohms, X was substantially zero, or negligibly small and p was varied from 0 to 26. The resultant change in the magnitude of Zs was from 5930 to 6620 ohms, giving an average value of 6275 ohms, with a variation of or 5.5% from this value.

Let us now consider the constancy of the is contained in the term x -(-2 (1- p) v in which the factor (1-cos 2p) varies from unity to a rather .small value, as the value-of'p in-- to a rather small value, as the value of p increases above 0. The factor (1l-2) shows that this variation could be made 0, no matter what the value of the angle :2, if the transformation-ratio n=2. If n is less than 2, the sign of the factor (n-2) becomes negative, so that the coeflicient A decreases, instead of increasing, with increasing values of the angle 4:. If the transformationratio n only slightly greater than 2, so that the factor (n-2) is a fraction less than 0.732, the coefficient A increases, with increasing values of the angle 9, but at a rate determined by the expression given in Equation 9.

In the aforesaid actual embodiment of my invention, I utilized a transformation-ratio of n=2.33, which theoretically made A vary from' 1.00 to 1.07, whenp varied from 0 to 26.

These calculations have taken no account of saturation in the iron core of the phase-shifting transformer T, the eil'ect of which would be to reduce the transformer-reactances Xi and Xi, and also to introduce a leakage-factor reducing the mutual coupling M to a value somewhat less than v xixa, as the primary current Ii was increased in order to increase the primary-circuit impedance-angle p. As these saturation-effects enter into the valuation .of both the numerator A and the denominator Zs, they tend to cancel out, although the saturation-eflect is somewhat stronger in the numerator.

It will be noted that both the numerator A and the denominator Zs, of the coeillcient A/Zs. representing the magnitude-ratio of the response to the line-voltage E, become larger, as p increases from 0 to 26; the numerator A increasing by 7% of its original value, while the denominator Zs increases by 11.6%, theoretically, in the illustrated example. If the voltage-response were the only consideration, it is obvious that these increases in A and Zs could be equalized, by making a transformation-ratio n slightly larger than 2.33. For example, if itwere desired to make the numerator A increase by 12%, when the angle p increased from 0 to 26, A could be put equal to 1.12 in Equation 9, yielding n=2.52. In general, the transformation-ratio 12 should be between 2 and 2.5.

If, however, any particular applicationor-my invention requires a constant'ratio between the current-responsive component KI/Zs, and the voltage-responsive component AEI/Zs, in Equation (20), or a constant ratio K/A, at diflerent values of the phase-shift angle a, then the variation in the coeflicient A of my phase-shifting network I would have to be as small as possible, all things considered. In such a case, the first mentioned transformation-ratio, n= 2.33 would be a better compromise, because it would split the 6% average-error in Zs, (or 12% overall-error), leaving something like the same amount of error in A as in the ratio A/Zs, making A constant within plus or minus 3%%, and A/Zs constant within plus or minus 3%. as the phase-shift angle, a,

is adjusted between the limits, 0 and 60.

Thus, in the previously mentioned Golds numerator A of the magnitude-coemoient A/Zs 1s borough application, the relaying-current is at line-current 1, or being equal, say to Me The balance-point ot the relay occurs whenthese two fluxes are equal in magnitude, or when Iz=l (21) From Equation it is evident that I: is equal to the absolute value or the vector-dinerence which is included in the brackets. This vector-dlflerence has the magnitude Ia and also some vector-angle, which we may call a. Hence we may express this bracketed quantity as follows, and we may make the substitution sho n in Equation (21), yielding Dividing through by the absolute value of the and having a radius gZs/A, at varying values of the linepower-iactor angle 0, and at any constant value of the current-response angle 1: and the voltage-response angle a.

It wil be noted that the displacement-angle of the center of the circle represented in Equation (25) is the angle (k-a) which is the phase-displacement between the voltage-responsive component Eco/ZS and the current-responsive component Ere/2s at unity power-factor. Either I: or a may be varied; that is, either the phase-displacement a of the voltage-response, or the phasedisplacement k of the current-response. The illustrated embodiment of my invention shows the adjustable angle a. in the voltage-responsive input of the relay or load-device 2, but I desire it to be understood'that it could have been introduced in the current-responsive voltage K121 instead of the voltage responslve voltage E.

The variable part of the phase-shitt ot the voltage-responsive component Eee/Zs, with respect to the current-responsive component Eat/2s oi the relay iz, as produced by my phase-shitting network I, is the angle a, which is evaluated in Equation (10). From this equation, and also from Equation (8) it is apparent that, when the transformation-ratio n has the critical value of 2,

the phase-shirt angle a is equal to exactly 2 times the primary circuit impedance-angle p, but opposite in sign. For a 26 variation in the primary angle p, this would yield only a 52 shift in voltage, either leading or lagging with respect to the impressed voltage E, depending upon the polarity of the transformer-connections.

lithe transformation-ratio n ismade smaller than 2, Equation 10 shows that a definite amount 2 (i-' representing the tangent 0! (2p) regardless oi the value 9, meaning that the phase-shift angle a will have a numerical angle less than 29.

It the transformation-ratio n is greater than 2, the constant quantity must be subtracted irom the denominator of the traction representing the tangent of (--2p) in Equation 10, meaning that the phase-shift angle a has a numerical value greater than 2p. In the numerical example previously given with n=2.33, the theoretical value of the phase-shift angle a, neglecting saturation, is 59.1", when the primary-circuit angle p=26. It is thus seen that an advantage is gained, in the way of a greater range of phase-shirt angle a, by making the transformation-ratio n as much greater than 2 as can be tolerated, without introducing too much error in the magnitude-ratio A of the voltageresponse or output-voltage oi the network.

I claim as my invention:

1. A phase-shifting network for deriving a voltage of a shifted phase and an approximately unchanged magnitude from an alternating-current line which has voltage-supplying means for supplying a line-derived input-voltage which is dependent upon a voltage of the line, substantially unaiiected by the impedance of the burden on said voltage-supplying means within the normal burden-range thereof, said network comprising a pair of input-terminals for' supplying said inputvoltage to the network, a pair 0! output-terminals,

a phase-shifting transformer having a primary circuit and a secondary circuit, an independently variable resistor, said secondary circuit being connected between one of said input-terminals and one of said output-terminals, circuit-connections joining the other output-terminal to the other input-terminal, and circuit-connections for connecting said variable resistor in series with said primary circuit for energization across the two s input-terminals, the minimum adjustable value 55 age of a shifted phase and an approximately unchanged magnitude from an alternating-current line which has voltage-supplying means for supplying a line-derived input-voltage which is dependent upon a voltage of the line, substantially so unaffected by the impedance of the burden on said voltage-supplying means within the normal burden-range thereof, said network comprising a pair oi input-terminals for supplying said inputvoltage to the network, a pair of output-terminals,

as a phase-shitting transformer having a primary circuit and a secondary circuit, an independently variable resistor, said secondary circuit being connected between one of said input-terminals and one of said output-terminals, circuit-connections Joining the other output-terminal to the other input-terminal, and circuit-connections for connecting said variable resistor in series with said primary circuit for energization across the two input-terminals, the minimum adjustable 15 value oi saidvariableresistor being greater than is added to the denominator or the traction transformer having a small leakage between a primary and secondary turns, and the ratio of the secondary turns to the primary turns of the phase-shifting transformer being between approximately 2 and approximately 2.5.

3. A phase-shifting network for deriving a voltage of a shifted phase and an approximately unchanged magnitude from an alternating-current line which has voltage-supplying means for supplying a line-derived input-voltage which is dependent upon a voltage of the line, substantially unaffected by the impedance ofthe burden on said voltage-supplying means within the normal burden-range thereof, said network comprising a pair of input-terminals for supplying said inputvoltage to the network, a pair of output-terminals, a phase-shifting transformer having a primary circuit and a secondary circuit, an independently variable resistor, said secondary circuit being connected between one of said input-terminals and one of said output-terminals, circuit-connections joining the other output-terminal to the other input-terminal, and circuit-connections for connecting said variable resistor in series with said primary circuit for energization across the two input-terminals, the phase-shifting transformer having a small leakage between primary and secondary turns, and the ratio of the secondary turns to the primary turns of the phaseshifting transformer being between approxi mately 2 and approximately 2.5.

4. A phase-shifting network for deriving a voltage of a shifted phase and an approximately unchanged magnitude from an alternating-current line which has voltage-supplying means for supplying a line-derived input-voltage which is dependent upon a voltage of the line, substantially unaffected by the impedance of the burden on said voltage-supplying means within the normal burden-range thereof, said network comprising a pair of input-terminals for supplying said inputvoltage to the network, a pair of output-terminals, a phase-shifting transformer having a primary circuit and a secondary circuit, an independently variable resistor, said secondary circuit being connected between one of said input-terminals and one of said output-terminals, circuit-connections joining the other output-terminal to the other input-terminal, and circuit-connections for connecting said variable resistor in series with l0 6.1'heinventionaadeflnedinciaimlLcharacteriaed by the circuit which includes said aeoondarycircuit ofthephase-shiftingtransformerandthelcad-devicehavinganimpedance whichislargeenoughtoswampanyvariations intheeii'ectiveimpedanceoftheaecondinput-' voltage when the latter is independently adjusted in magnitude, whereby the total impedance re-. mains substantially constant in magnitude, within permissible limits of error.

7. The inventionas defined in claim 5. charfacteriud by.the circuit which includes said secondary circuit of the phase-shifting tramformer and the load-device having an impedance whichislarge enoughtoswampanyvariations in the effective impedance of the second Inpu voltage whenthe latter is independently adjusted in magnitude, whereby the total impedance remains substantially constant in magnitude, within permissible limits of error, said invention being further characterized by the minimum adjustable value'of said variable resistor being greater than 1.7 times the primary inductive 'reactance of the phase-shifting transformer.

8. The invention as defined in claim 5, characterized by the circuit which includes said secondary circuit of the phase-shifting transformer and the load-device having an impedance which is large enough to swamp any variations in the elective impedance of the second inputwoltage when the latter is independently adjusted in magnitude, whereby the total impedance remains substantially constant in magnitude, within permissaid primary circuit for energization across the and secondary turns, and the ratio of the secondary turns to the primary turns of the phaseshifting transformer being approximately 2.

5. A phase-shifting network for use with an alternating-current line having means for supplying two separate input-voltages to said network from said line, said network comprising a phase-shifting transformer having a primary circuit and a secondary circuit, a variable primarycircuit resistor, circuit-connections for serially connecting said two input-voltages and the secondary circuit of said phase-shifting transformer in series with a load-device, circuit-connections for connecting said variable primarycircuit resistor in series with the primary circuit of said phase-shifting transformer for energizetion in shunt-circuit relation to one of said inputvoltages, and means for independently varying sible limits of error, said invention being further characterized by the minimum adjustable value of said variable resistor being greater than 1.! times the primary inductive reactance of the phaseshifting transformer, the phase-shifting transformer having a small leakage between primary and turns, and the ratio of the secondaryturnstotheprimaryturnsofthephase-shifting transformer being between approximately 2 and approximately 2.5.

9. The invention as defined in claim 5. characterized by the circuit which includes said secondary circuit of the phase-shifting transformer and the load-device having an impedance which is large enough to swamp any variations in the effective impedance of the second input-voltage when the latter is independently adjusted in magni tude, whereby the total impedance remains substantially constant in magnitude, within permissible limits of error, said invention being further characterized by the phase-shifting transformer having a small leakage between primary and secondary turns, and the ratio of the secondary turns to the primary turns of the phase-shifting transformer being between approximately 2 and approximately 2.5.

10. The invention as defined in claim 5, characteriaed by the circuit which includes said secondary circuit of the phase-shifting transformer and the load-device having an impedance which is large enough to swamp any-variations in the eflective impedance of the input-voltage when the latter is independently-adjusted in magnitude, whereby the total impedance remains substantially constant in magnitude, within permissible limits of error, said invention being further characterized by the phase-shifting transformer having a small leakage between primary and secondary turns, and the ratio of the secondary turns to the primary turns of the phase-shifting 76 transformer being approximately 2.

11. The invention as defined in claim 5, characterized by the minimum adjustable value of.

said variable resistor being greater than 1.7 times the primary inductive reactance cf the phaseshifting transformer.

. 12. The invention as defined in claim 5, characterized by the minimum adjustable value of said variable resistor being greater than 1.7 times the primary inductive reactance of the phase-shifting transformer, the phase-shifting transformer having a small leakage between primary and secondary turns, and the ratio of the secondary turns to the primary turns of the phase-shifting transformer being between approximately 2 and approximately 2.5.

13. The invention as defined in claim 5, characterized by the phase-shifting transformer having a small leakage between primary and secondary turns, and the ratio of the secondary turns to the primary turns of the phase-shifting transformer being approximately 2.

HERBERT J. CARLIN.

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

UNITED STATES PATENTS Number Name Date 2,224,067 Sprong Dec. 3, 1940 2,234,746 west Mar. 11, 1941

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