A Method of and Means for Deriving Two or More Alternating Currents of Different Phase from a Source of Single Phase Electrical Supply.
Year: 1899

page_text: Date of Application, 17th Jan., 1899
Complete Specification Left, 13th Oct., 1839-Accepted, 18th Nov., 1899
A Method of and Means for Deriving Two or More Alternating Currents
of Different Phase from a Source of Single Phase Electrical Supply.
I, HERBERT APPLETON WAGNER, a Citizen of the United States of America,
residing at 4125, Delmar Boulevard, St. Louis, in the State of Missouri,
Electrical Engineer, do hereby declare the nature of this invention to be as
follows:-
This invention relates to a method of and means for deriving two or more
alternating currents differing from one another in phase from a source of elec.
tricity supplying alternating currents of single phase.
It is well known that in circuits containing self induction, the current lags
behind the electromotive force by a certain angle depending upon the relative
ohmic and inductive resistances.
The current flowing in such a circuit may be considered as due to the resultant
of two electro-motive forces, one being that which would be sufficient to cause
the same flow of current through the ohmic resistance, and the other that which
would be required to overcome the electro-motive force of self induction or the
inductance. These two electro-motive forces always differ in phase by an angle
of ninety degrees, and with their resultant may be conveniently represented
graphically by the three sides of a right-angled triangle.
Slight differences of phase have been heretofore produced between two cir-
cuits derived from the same single phase source by introducing self induction
into one of them and non-inductive resistance into the other. Only slight phase
differences are obtainable in this way, however, it being impossible to even
approximate or approach a difference as great as ninety degrees, as this would
require an infinite electro-motive force and an indefinite inductive resistance.
To produce phase differences in this way which could be effectively applied for
any purpose such as starting or operating alternating current motors very much
higher electro-motive forces must be obtained than are required on the working
circuits, and these electro-motive forces then cut down by the necessary ohmic
and inductive resistances, resulting in a large loss of energy and an unwarrant-
able increase in the capacity of generator, lines and transformers.
As all alternating current motors have a large self-inductive element in their
coils, if the method just described is used in connection with such motors, a still
smaller phase angle can be secured, the self-contained inductance counteracting.
in part the effect of that extraneously applied. I have found that any number
of circuits differing by almost any desired amount in phase may be derived
from two circuits differing slightly in phase or made to differ by such ordinary
means described, by connecting the required circuits between suitable points in
the two given circuits, and that this may be accomplished with practically no
loss of energy.
In the accompanying drawings, Figs. 1, 2 and 5 are diagrams serving to

page_text: illustrate graphically the principle of my invention. Figs. and 4 illustrate
the manner of operating two and three phase motors respectively by means of
my invention.
In Fig. 1, A D represents in direction and amount the electro-motive force of
a source of alternating current or an alternating current derived therefrom, such
as the secondary of a transformer, CD the electro-motive force across the terminals
of an inductance coil forming a derived circuit differing in phase from the electro-
motive force AD by the angle ADC and AC the resultant electro-motive force
across the terminals of a working circuit derived from the source A D and made
to differ from it by the angle CAD, through the effect of the inductance CD.
The greatest angle of phase difference which could be obtained by methods
heretofore known may be represented by the angle CAD between the circuits AC
and A D. If another circuit is connected from the point C to some point E on
AD, an angle ACE is formed with the circuit AC. This angle represents the
difference of phase between the derived circuit AC and CE. The point E may
,be moved in either direction along AD to any other position as E¹ and the
phase relation of CE as well as its relative electro-motive force be altered as
desired.
It is evident that any number of circuits may be connected to as many different
points in this way, forming angles of phase difference ACE, ACE, etc., with
A C, and the angles CEA, CEA, etc. with AD. The electro-motive force AC
is represented as that which would occur across the terminals of a circuit con-
taining some self-induction, such as the coils of an alternating current motor,
in which BC is the electro-motive force of self-induction and AB the electro-
motive force required to send the given current through the ohmic resistance
of the wire and against the counter-electro-motive force caused by the rotation
of the motor. A B, the non-inductive element of the circuit will always be at
right angles to the inductance CD.
The use of the same lines to represent both the resultant clectro-motive forces
of working circuits and also the circuits themselves need not lead to confusion
to one practiced in the art and accustomed to representing electrical phenomena
graphically. As the currents in phase and amount in circuits of similar in-
ductance or self induction are determined by the electro-motive forces across the
terminals of such circuits, we can simplify the representation of the phase
differences of such circuits by showing simply the electro-motive forces.
The line CE represents an electro-motive force across the terminals of a
second working circuit such as another set of coils of a polyphase motor. Its
magnitude and phase are determined by the relative magnitudes and phases
of the electro-motive forces AC, CD, and A E. The point C being fixed by
the relation of the electro-motive forces AC, CD, and AD. The new electro-
motive force CE across the new working circuit can be derived by connecting
such new working circuit between C and some point, as E, on the transformer
coil represented by the electro-motive force AD. It is clear that this new
electro-motive force can be varied in phase and magnitude by moving its point
of connection along the line A 1) in either direction. The method of securing
the phase relations between A C, CD, and A D is a well known one.
FE represents the electro-motive force necessary to send the current through
the non-inductive resistance, and F C is the electro-motive force of self induction
at right angles to FE. It will be noticed that FE, which may also represent
the phase of the current, bears the same phase relation to AE that CE bears
to AC. It is therefore seen that the relative phases of the currents in the
working circuits described are determined by the relative phases of the electro-
motive forces across those working circuits.
If there is no self induction in the circuit A C, it will assume the position A B
at right angles to BD, and the relative phase angles and magnitude then
acquired by the different circuits are shown in Fig. 2. This condition would
not be likely to exist, however, in any combination of circuits in which currents

page_text: differing in phase would be used. It being assumed in this figure that the
working circuits A B-and-B E have no self induction, the lines A B and B E
truly represent the phase relations between those two working circuits both as
to electromotive force and current.
The flow of a comparatively large amount of current in a derived circuit, such
as CE will cause a slight decrease in the angle CAD by the nearer approach
of C to D. This can be corrected by increasing the inductance CD, or the
phase relations between AC and CE can be retained by moving the point of
connection E.
Fig. 3 shows the application of the principle to the operation of a two phase
motor. T is a transformer with secondary coil A D. M is a motor with its
two circuits or sets of coils X Y and joined at C, and with their other terminals
connected one to A and the other to E, and I an inductance coil connected
between C and D). The designating letters being the same as in Fig. 1, the phase
angles can be readily traced.
In Fig. 4, M represents a three-phase motor with sets of coils X, Y and Z. The
coils Y and Z are joined at C, their other ends being connected to the transformer
at A and E respectively. The coil X is connected between the trans-
former terminals A and E, and the junction C is connected to the
other transformer terminal D through the inductance coil I.
Fig. 5
shows graphically the phase angles obtained in the arrangement illus-
trated in Fig. 4, the same designating letters being employed as in the
preceding figures.
11
1
יז'
1000
J. G. LORRAIN, M.I.E.E., &c.,
Norfolk House, Norfolk Street, London, W.C.,
Chartered Patent Agent.
A Method of and Means for Deriving Two or More Alternating Currents
of Different Phase from a Source of Single Phase Electrical Supply.
I, HERBERT APPLETON WAGNER, a Citizen of the United States of America,
residing at 4125, Delmar Boulevard, St. Louis, in the State of Missouri,
Electrical Engineer, do hereby declare the nature of this invention and in what
nanner the same is to be performed, to be particularly described and ascertained
in and by the following statement:―
This invention relates to a method of and means for deriving two or more
alternating currents differing from one another in phase from a source of elec
tricity supplying alternating currents of single phase.
It is well known that in circuits containing self induction, the current lags
behind the electromotive force by a certain angle depending upon the relative
ohmic and inductive resistances.
The current flowing in such a circuit may be considered as due to the resultant
of two electro-motive forces, one being that which would be sufficient to cause
the same flow of current through the ohmic resistance, and the other that which
would be required to overcome the electro-motive force of self induction or the
inductance. These two electro-motive forces always differ in phase by an angle
of ninety degrees, and with their resultant may be conveniently represented
graphically by the three sides of a right-angled triangle.

page_text: Slight differences of phase have been heretofore produced between two cir-
cuits derived from the same single phase source by introducing self induction
into one of them and non-inductive resistance into the other. Only slight phase
differences are obtainable in this way, however, it being impossible to even
approximate or approach a difference as great as ninety degrees, as this would
require an infinite electro-motive force and an indefinite inductive resistance.
To produce phase differences in this way which could be effectively applied for
any purpose such as starting or operating alternating current motors very much
higher electro-motive forces must be obtained than are required on the working
circuits, and these electro-motive forces then cut down by the necessary ohmic
and inductive resistances, resulting in a large loss of energy and an unwarrant-
able increase in the capacity of generator, lines and transformers.
As all alternating current motors have a large self-inductive element in their
coils, if the method just described is used in connection with such motors, a still
smaller phase angle can be secured, the self-contained inductance counteracting
in part the effect of that extraneously applied. I have found that any number
of circuits differing by almost any desired amount in phase may be derived
from two circuits differing slightly in phase or made to differ by such ordinary
means described, by connecting the required circuits between suitable points in
the two given circuits, and that this may be acconiplished with practically no
loss of energy.
In the drawings left with my provisional specification, Figs. 1, 2 and 5 are dia-
grams serving to illustrate graphically the principle of my invention. Figs. 3 and 4
illustrate the manner of operating two and three phase motors respectively by
means of my invention.
In Fig. 1, A D represents in direction and amount the electro-motive force of
a source of alternating current or an alternating current derived therefrom, such
as the secondary of a transformer, CD the electro-motive force across the terminals
of an inductance coil forming a derived circuit differing in phase from the electro-
motive force AD by the angle ADC and AC the resultant electro-motive force
across the terminals of a working circuit derived from the source AD) and made
to differ from it by the angle CAD, through the effect of the inductance CD.
The greatest angle of phase difference which could be obtained by methods
heretofore known may be represented by the angle CAD between the circuits AC
and A D. If another circuit is connected from the point C to some point E on
AD), an angle ACE is formed with the circuit A C. This angle represents the
difference of phase between the derived circuit AC and CE. The point E may
be moved in either direction along AD to any other position as E' and the
phase relation of CE as well as its relative electro-motive force be altered as
desired.
It is evident that any number of circuits may be connected to as many different
points in this way, forming angles of phase difference ACE, ACE, etc., with
A C, and the angles CEA, CEI A, etc. with AD. The electro-motive force A C
is represented as that which would occur across the terminals of a circuit con-
taining some self-induction, such as the coils of an alternating current motor,
in which BC is the electro-motive force of self-induction and AB the electro-
motive force required to send the given current through the ohmic resistance
of the wire and against the counter-electro-motive force caused by the rotation
of the motor. A B, the non-inductive element of the circuit will always be at
right angles to the inductance CD.
The use of the same lines to represent both the resultant electro-motive forces
of working circuits and also the circuits themselves need not lead to confusion
to one practiced in the art and accustomed to representing electrical phenomena
graphically. As the currents in phase and amount in circuits of similar in-
ductance or self induction are determined by the electro-motive forces across the
terminals of such circuits, we can simplify the representation of the phase
differences of such circuits by showing simply the electro-motive forces.

page_text: The line CE represents an electro-motive force across the terminals of a
second working circuit such as another set of coils of a polyphase motor. Its
magnitude and phase are determined by the relative magnitudes and phases
of the electro-motive forces AC, CD), and AE. The point C being fixed by
the relation of the electro-motive forces AC, CD, and A D. The new electro-
motive force CE across the new working circuit can be derived by connecting
such new working circuit between C and some point, as E, on the transformer
coil represented by the electro-motive force AD. It is clear that this new
electro-motive force can be varied in phase and magnitude by moving its point
of connection E along the line A D in either direction. The method of securing
the phase relations between A C, C D), and A D is a well known one.
FE represents the electro-motive force necessary to send the current through
the non-inductive resistance, and F C is the electro-motive force of self induction
at right angles to FE. It will be noticed that FE, which may also represent
the phase of the current, bears the same phase relation to AE that CE bears
to AC. It is therefore seen that the relative phases of the currents in the
working circuits described are determined by the relative phases of the electro-
motive forces across those working circuits.
If there is no self induction in the circuit A C, it will assume the position A B
at right angles to BD, and the relative phase angles and magnitude then
acquired by the different circuits are shown in Fig. 2. This condition would
not be likely to exist, however, in any combination of circuits in which currents
differing in phase would be used. It being assumed in this figure that the
working circuits A B and B E have no self induction, the lines A B and B E
truly represent the phase relations between those two working circuits both as
to electromotive force and current.
The flow of a comparatively large amount of current in a derived circuit, such
as CE will cause a slight decrease in the angle CAD by the nearer approach
of C to D. This can be corrected by increasing the inductance CD, or the
phase relations between AC and CE can be retained by moving the point of
connection E.
Fig. 3 shows the application of the principle to the operation of a two phase
motor. T is a transformer with secondary coil A D. M is a motor with its
two circuits or sets of coils XY and joined at C, and with their other terminals
connected ene to A and the other to E, and I an inductance coil connected
between C and D). The designating letters being the same as in Fig. 1, the phase
angles can be readily traced.
In Fig. 4, M represents a three-phase motor with sets of coils X, Y and Z. The
coils Y and Z are joined at C, their other ends being connected to the transformer
at A and E respectively. The coil X is connected between the trans-
former terminals A and E, and the junction C is connected to the
other transformer terminal D through the inductance coil I. Figure 5
shows graphically the phase angles obtained in the arrangement illus-
trated in Figure 4, the same designating letters being employed as in the
preceding figures.
Having now particularly described and ascertained the nature of my said
invention and in what manner the same is to be performed, I declare that what
I claim is: -
1. The method of obtaining difference in phase between two or more alternating
current branch circuits, which consists in connecting said branch circuits to
different points in a single phase supply circuit and to each other, and shifting
the phase of one of said branch circuits, whereby a slight phase difference in said
branch circuit will cause currents to flow through the other of said branch circuits
differing in phase from one another and from the supply circuit.
2. The method of obtaining difference of phase between alternating current
circuits supplied from the same single phase source, which consists in inducing

page_text: between said source and a branch circuit derived therefrom a slight difference
of phase by introducing self induction into said branch circuit, and then con-
necting other desired branch circuits between other properly selected points on
said source and its said branch derived therefrom, whereby currents in the said
desired branch circuits will be made to differ in phase from currents in said
source, its said derived branch circuit and from one another, by angles of the
required phase difference.
3. The method of obtaining difference of phase between two or more alternating
current derived circuits, which consists in joining together one end of each of said
circuits, connecting the common junction thus formed through suitable inductance
or inductive resistance to a point in a main supply circuit, and connecting the
other ends of said circuits each to a different point in said supply circuit, whereby
the difference of potential between such points of connection will determine the
desired phase difference between the said circuits.
4. The method of inducing in two or more circuits, a flow of alternating currents
differing in phase from one another, which consists in attaching one end of
each of said circuits each to a different point in a main supply circuit, such points
differing in potential from one another by a pre-determined amount, joining the
other ends of the said circuits together, and electrically connecting the common
junction thus formed, through an inductance or inductive resistance, to another
point in the main supply circuit differing in potential from the points before
selected.
5. In a system of electrical distribution, a single phase source of alternating
currents, a circuit derived therefrom having its phase slightly shifted and con-
nected to the source at a given point, and one or more branches connected to
suitable points in the said derived circuit and to points on the source differing
in potential from each other and from the said point of connection of the said
derived circuit.
6. In a system of electrical distribution by alternating currents, a single phase
source, a circuit derived therefrom containing self-induction, other branch cir-
cuits connected between suitable points on the derived circuit and points on the
source differing in potential from the point of junction of said source and its
said derived circuit.
7. In a system of electrical distribution, a supply circuit of alternating currents,
circuits derived therefrom having one of the ends of each joined together and
the other ends thereof each connected to a different point on said supply circuit,
and a circuit containing suitable inductive resistance connecting the common
junction so formed to the supply circuit at a point differing in potential from the
said points of connection of said derived circuits.
8. In a system of electrical distribution, a supply circuit of alternating currents,
circuit derived therefrom having one end of each connected to a different point
in said supply circuit, said points differing in potential from one another by a
pre-determined amount, the other ends of said derived circuits being suitably
joined, and a circuit containing suitable inductive resistance electrically connect-
ing the junction so formed to another point in the supply circuit differing in
potential from the points before selected.
Dated this 13th day of October 1800.