177. The magnetic circuit of the induction motor at or near synchronism consists of two magnetic fluxes superimposed upon each other in quadrature, in time, and in position. In the polyphase motor these fluxes are produced by e.m.fs. displaced in phase. In the monocyclic motor one of the fluxes is due to the primary power circuit, the other to the primary exciting circuit. In the single-phase motor the one flux is produced by the primary circuit, the other by the currents produced in the secondary or armature, which are carried into quadrature posi- tion by the rotation of the armature. In consequence thereof, while in all these motors the magnetic distribution is the same at or near synchronism, and can be represented by a rotating field of uniform intensity and uniform velocity, it remains such in polyphase and monocyclic motors; but in the single-phase motor, with increasing slip - that is, decreasing…
Symbolic AC Method Passage Atlas
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Why This Theme Matters
Section titled “Why This Theme Matters”This passage may show how Steinmetz turns phase geometry into calculable electrical algebra.
Candidate Passages
Section titled “Candidate Passages”Consequently, in the polyphase motor running synchronously, that is, doing no work whatever, the secondary becomes current- less, and the primary current is the exciting current of the motor only. In the single-phase induction motor, even when running light, the secondary still carries the exciting current of the mag- netic flux in quadrature with the axis of the primary exciting coil. Since, this flux has essentially the same intensity as the flux in the direction of the axis of the primary exciting coil, the current in the armature of the single-phase induction motor run- ning light, and therefore also the primary current corresponding thereto, has the same m.m.f., that is, the same intensity, as the primary exciting current, and the total primary current of the single-phase induction motor running light is thus twice the exciting current, that is, it is the exciting current of the main magnetic flux p…
In consequence of the relative motion of the primary and secondary, the magnetic circuit of the induction motor must be arranged so that the secondary while revolving does not leave the magnetic field of force. That means, the magnetic field of force must be of constant intensity in all directions, or, in other words, the component of magnetic flux in any direction in space be of the same or approximately the same intensity but differing in phase. Such a magnetic field can either be considered as the superposition of two magnetic fields of equal intensity in quad- rature in time and space, or it can be represented theoretically by a revolving magnetic flux of constant intensity, or rotating
The inductively compensated series motor with secondary ex- citation, or inverted repulsion motor, 3, takes an intermediary position between the series motors and the repulsion motors; it is a series motor in so far as the armature is in the main supply circuit, but magnetically it has repulsion-motor characteristics, that is, contains a lagging quadrature flux. As the field exci- tation consumes considerable voltage, when supplied from the compensating winding as secondary circuit, considerable voltage must he generated in this winding, thus giving a corresponding transformer flux. With increasing speed and therewith decreas- ing current, the voltage consumed by the field coils decreases, and therewith the transformer flux which generates this voltage. Therefore, the inverted repulsion motor contains a transformer flux which has approximately the intensity and the phase re- quired for commutation; it la…
A part of this magnetic flux (lines a in Fig. 111-4) interlinks with the armature circuit only, that is, is true self-inductive or leakage flux. Another part, however, (6) interlinks with the field also, and thus is mutual inductive flux of the armature cir- cuit on the field circuit. In a polyphase machine, the resultant armature flux, that is, the resultant of the fluxes. Fig. Ill, of all phases, revolves synchronously at (approximately) constant in- tensity, as a rotating field of armature reaction, and, therefore, is stationary with regard to the synchronously revolving field, F, Hence, the mutual inductive flux of the armature on the field, though an alternating flux, exerts no induction on the field circuit, is indeed a unidirectional or constant flux with regards to the field circuit. Therefore, under stationary conditions of load, no difference exists between the self-inductive and the mutual in-…
The alternation of the field flux induces an e.m.f. of self induction in the field winding. In the shunt motor, this causes the field exciting current and with it the magnetic field flux to lag and thereby to be out of phase with the armature current which, to represent work, must essentially be an energy current, and thereby reduces output and efficiency and hence requires some method of compensation, as capacity in series with the field winding or excitation of the field from a quadrature phase of voltage. In the series motor the self-inductance of the field causes the main current to lag behind the impressed voltage and thereby lowers the power-factor of the motor. Thus, to get good power-factor, the field self-inductance must be made low, that is, the field as weak and the armature as strong as possible. With such a strong armature, and weak field, the commutating pole is not sufficient to control ma…
67. In the theoretical investigation of electric circuits the velocity of propagation of the electric field through space is usually not considered, but the electric field assumed as instan- taneous throughout space; that is, the electromagnetic com- ponent of the field is considered as in phase with the current, the electrostatic component as in phase with the voltage. In reality, however, the electric field starts at the conductor and propa- gates from there through space with a finite though very high velocity, the velocity of light; that is, at any point in space the electric field at any moment corresponds not to the condi- tion of the electric energy flow at that moment but to that at a moment earlier by the time of propagation from the conductor to the point under consideration, or, in other words, the electric field lags the more, the greater the distance from the conductor.
80. Alternating-current motors are usually single-phase, since the possibility of commutation control makes the single-phase easier than a polyphase design. In the single-phase motor, the magnetic field flux is constant in direction, and the direction in quadrature to the main field flux thus is available for pro- ducing a suitable commutating flux. In the polyphase motor, however, the magnetic flux rotates, assuming successively all directions, and thus no commutating flux can be used. For this reason, designs of polyphase commutator motors have been made in which the different (2 and 3) phases are kept separate, and spaces left between them for accommodating commutating fluxes.
134. The operation of the induction motor thus can also be considered as due to the action of a rotating magnetic field upon a system of short-circuited conductors. In the motor field or primary, usually the stator, by a system of polyphase impressed e.m.fs. or by the combination of a single-phase impressed e.m.f. and the reaction of the currents produced in the secondary, a rotating magnetic field is produced. This rotating field produces currents in the short-circuited armature or secondary winding, usually the rotor, and by its action on these currents drags along the secondary conductors, and thus speeds up the armature and tends to bring it up to synchronism, that is, to the same speed as the rotating field, at which speed the secondary currents would disappear by the armature conductors moving together with the rotating field, and thus cutting no lines of force. The secondary therefore slips in spe…
The direction of rotation of a direct-current motor, whether shunt or series motor, remains the same at a reversal of the im- pressed e.m.f., as in this case the current in the armature circuit and the current in the field circuit and so the field magnetism both reverse. Theoretically, a direct-current motor therefore could be operated on an alternating impressed e.m.f. provided that the magnetic circuit of the motor is laminated, so as to fol- low the alternations of magnetism without serious loss of power, and that precautions are taken to have the field reverse simul- taneously with the armature. If the reversal of field magnetism should occur later than the reversal of armature current, during the time after the armature current has reversed, but before the field has reversed, the motor torque would be in opposite direc- tion and thus subtract; that is, the field magnetism of the alter- nating-curren…
81. If in a direct-current motor, at constant impressed voltage, the field excitation and therefore the field magnetism is decreased, the motor speed increases, as the armature has to revolve faster to consume the impressed e.m.f., and if the field excitation is increased, the motor slows down. A synchronous motor, however, cannot vary in speed, since it must keep in step with the impressed frequency, and if, therefore, at constant impressed voltage the field excitation is decreased below that which gives a field magnetism, that at the synchronous speed consumes the impressed voltage, the field magnetism still must remain the same, and the armature current thus changes in phase in such a manner as to magnetize the field and make up for the deficiency in the field excitation. That is, the armature current becomes lagging. Inversely, if the field excitation of the synchronous motor is increased, the magnet…
The magnetic field of any induction motor, whether supplied by polyphase, monocyclic, or single-phase e.m.f., is at normal condition of operation, that is, near synchronism, a polyphase field. Thus to a certain extent all induction motors can be called polyphase machines. When supplied with a polyphase system of e.m.fs. the internal reactions of the induction motor are simplest and only those of a transformer with moving second- ary, while in the single-phase induction motor at the same time a phase transformation occurs, the second or magnetizing phase being produced from the impressed phase of e.m.f. by the rota- tion of the motor, which carries the secondary currents into quadrature position with the primary current.
Exciting admittance in the induction motor, and synchronous impedance in the synchronous motor, are corresponding quanti- ties, representing the magnetizing action of the armature cur- rents. In the induction motor, in which the magnetic field is produced by the magnetizing action of the armature currents, very high magnetizing action of the armature current is desirable, so as to produce the magnetic field with as little magnetizing cur- rent as possible, as this current is lagging, and spoils the power- factor. In the synchronous motor, where the magnetic field is produced by the direct current in the field coils, the magnetizing action of the armature currents changes the resultant field excita- tion, and thus requires a corresponding change of the field current to overcome it, and the higher the armature reaction, the more
The shunt motor on an alternating-current circuit has the objection that in the armature winding the current should be power current, thus in phas£ with the e.m.f., while in the field winding the current is lagging nearly 90 deg., as magnetizing current. Thus field and armature would be out of phase with each other. To overcome this objection either there is inserted in series with the field circuit a condenser of such capacity as to bring the current back into p>hase with the voltage, or the field may be excited from a separate e.m.f. differing 90 deg. in phase from that supplied to the armature. The former arrange- ment has the disadvantage of requiring almost perfect con- stancy of frequency, and therefore is not practicable. In the latter arrangement the armature winding of the motor is fed by one, the field winding by the other phase of a quarter-phase sys- tem, and thus the current in the armature…
196. In those motor types in which a transformation of power occurs between compensating winding, C, and armature winding, A, a transformer flux exists in the direction of the brushes, that is, at right angles to the field flux. In general, therefore, the single-phase commutator motor contains two magnetic fluxes in quadrature position with each other, the main flux or field flux, A’, in the direction of the axis of the field coils, or at right angles to the armature brushes, and the quadrature flux, or transformer flux, or commu taring flux, *j, in line with the armature brushes, or in the direction of the axis of the compensating winding, that is, at right angles (electrical) with the field flux.
Since the resultant m.m.f. of the machine, which produces the flux, is the difference of the field excitation, Fig. 21 D and the armature reaction, then if the armature reaction shows an initial os- cillation, in Fig. 21 E, the field-exciting current must give the same oscillation, since its m.m.f. minus the armature reaction gives the resultant field excitation corresponding to flux $>. The starting transient of the polyphase armature reaction thus appears in the field current, as shown in Fig. 22(7, as an oscillation of full machine frequency. As the mutual induction between armature and field circuit is not perfect, the transient pulsation of armature reaction appears with reduced amplitude in the field current, and this reduction is the greater, the poorer the mutual inductance, that is, the more distant the field winding is from the armature wind- ing. In Fig. 22(7 a damping of 20 per cent is assume…
In direct current motors, commutation may be controlled by an interpole or commutating pole; that is, by producing a magnetic field at the brush, in direction opposite to the field of armature reaction, and by this field inducing in the arma- ture turn during commutation, an e. m. f. of rotation which reverses the current. Such a commutating pole, connected in series into a circuit, would, in the alternating current motor, induce an e. m. f. in the short circuited turn, by its rotation; but this e. m. f . would be in phase with the field of the commu- tating pole, and thus with the current, that is, with the main field of the motor. Therefore it could not neutralize the e. m. f. induced in the short circuited turn by the alternation of the main field through it, since this latter e. m. f. is in quadrature with the main field, and thus with the current; but would simply add itself to it, and so make the s…
In a three-phase generator, if the e. m. f . of one phase con- tains a third harmonic, as is usually the case, then by connect- ing the three phases in delta connection, the third harmonics of the generator e. m. f.’s are short circuited and so produce a triple frequency current circulating in the generator delta. This triple frequency circulating current can be measured by connecting an ammeter in one corner of the generator delta, and the sum of voltages of the three third harmonics can be measured by putting a voltmeter in a corner of the generator delta. This local current in the generator winding is the triple frequency voltage divided by the generator impedance (the stationary impedance, at triple frequency, but not the syn- chronous impedance, since the latter includes armature reac- tion). In generators of low impedance or close regulation, as turbine alternators, this local current may be far mo…
Since at or near synchronism, at the same impressed e.m.f. - that is, the same magnetic density - the total volt-amperes excitation of the single-phase induction motor must be the same as of the same motor on polyphase circuit, it follows that by operating a quarter-phase motor from single-phase circuit on one primary coil, its primary exciting admittance is doubled. Operating a three-phase motor single-phase on one circuit its primary exciting admittance is trebled. The self-inductive primary impedance is the same single-phase as polyphase, but the secondary impedance reduced to the primary is lowered, since in single-phase operation all secondary circuits corre- spond to the one primary circuit used. Thus the secondary impedance in a quarter-phase motor running single-phase is reduced to one-half, in a three-phase motor running single- phase reduced to one-third. In consequence thereof the slip of spee…
[[PDF_PAGE:49]] Report of Charles P. Steinmetz 43 Denotations e = nominal induced E. M. F. of alternator or group of alternators. Xii = true self inductive reactance of alternator or group of alter- nators. xn= external reactance of alternator or group of alternators, thus. Xi = xn+Xi2 = total self inductive reactance of alternators or group of alternators. xj = effective reactance of armature reaction of alternator or group of alternators, thus: Xo=xn+x 2 synchronous reactance of alternator or group of alternators. x = reactance (or impedance) between alternators. z = impedance of circuit between alternators. = Vi- 2+(2x!+x) 2 , where r = resistance of circuit between alternators. Or approximately a = phase angle of circuit between alternators, where: tan a = Or approximately : a = 90 degrees. w = phase displacement from mean, of oscillating alternators, thus: 2co = total phase displacement of oscillati…
phase system, the three voltages, currents, etc., are displaced in phase from each other by 120°. Their third harmonics therefore are displaced in phase from each other by 3 X 120°, that is, by 360°, or in other words, are in phase with each other. In Fig. 169, such triple frequency fluxes in the three cores would have no magnetic return, except by leakage through the air, that is, cannot exist, except in negligible intensity, and there- fore the core type of three-phase transformer cannot give any serious triple frequency voltage. In the shell type Fig. 168, however, the three triple frequency fluxes, being in phase with each other, produce a triple frequency single-phase flux through a closed magnetic circuit. Where the circuit conditions and connections are such as to give a triple harmonic - as with YY connection - the shell-type three-phase transformer may produce triple frequency voltages, resultin…
Similar transient phenomena also occur in space, that is, with space, distance, length, etc., as independent variable. Such transient phenomena then connect the conditions of the electric quantities at one point in space with the electric quantities at another point in space, as, for instance, current and potential difference at the generator end of a transmission line with those at the receiving end of the line, or current density at the surface of a solid conductor carrying alternating current, as the rail return of a single-phase railway, with the current density at the center or in general inside of the conductor, or the distribution of alternating magnetism inside of a solid iron, as a lamina of an alternating-current transformer, etc. In such transient phenom- ena in space, the electric quantities, which appear as functions of space or distance, are not the instantaneous values, as in the preceding…
extensively used, and monocyclic generators built. These were .^iriulr-pluisi’ alternating-eurrenl generators, having a small quadrature phase of high inductance, which combined with the main phase gives three-phase or quarter- phase voltages. The auxiliary phase was of such high reactance as to limit the quadra- < i < ti ■ poWCI and thus make the flow of energy essentially single- phase, that is, monocyclic. The purpose hereof was to permit the use of a small quadrature coil on the generator, and thereby to preserve the whole generator capacity for the single-phase main voltage, without danger of overloading the quadrature phase in case of a high motor load on the system. The genera] introduction of the three-phase system superseded the mono- cyclic generator, and monocyclic devices are today used only for local production of polyphase voltages from single-phase supply, for the starting of small siliEle…
In the series repulsion motors, 6 and 7, a quadrature field also exfsts, just as in the repulsion motors, but this quadrature field depends upon that part of the total voltage which is impressed upon the commutating winding, C, and thus can be varied by varying the distribution of supply voltage between the two cir- cuits; hence, in this type of motor, the commutating flux can be maintained through all (higher) speeds by impressing the total voltage upon the compensating circuit and short-circuiting the armature circuit for all speeds up to that at which the required commutating flux has decreased to the quadrature, flux given by the motor, and from this speed upward only a part of the supply voltage, inversely proportional (approximately) to the square of the speed, is impressed upon the compensating circuit, the rest shifted over to the armature circuit. The difference between 6 and 7 is that in 6 the…
by an opposite e. m. f. induced in this turn by its rotation through a quadrature field or commutating field, this field must therefore have the proper phase. The e. m. f. of alternation of the main field through the short circuited turn is proportional to the main field F and frequency N, and is in quadrature with the main field. The e. m. f. induced in the short circuited turn by its rotation (through the commutating field is proportional to the frequency of rotation or speed No, and to the commutating field Fo, and in phase therewith ; to be in opposition and equal to the e. m. f. of alternation, the commutating field must there- fore be in quadrature with the main field, and frequency times main field must equal speed times commutating field. That is :
The Brush machine in its principle essentially is a quarter- phase constant-current alternator with rectifying commutator. An alternator of low armature reaction and strong magnetic field regulates for constant potential: the change of armature reaction, resulting from a change of load, has little effect on the field and thereby on the terminal voltage, if the armature reaction is low. An alternator of very high armature reaction and weak field, however, regulates for constant current: if the m.m.f., that is, the ampere-turns required in the field coil to produce the magnetic flux, are small compared with the field ampere-turns required to take care of the armature reaction, and the resultant or magnetism-producing field ampere-turns thus the small difference between total field excitation and armature reaction, a moderate increase of armature current and thereby of armature reaction makes it equal to th…
Since at or near synchronism, at the same impressed E.M.F. - that is, the same magnetic density - the total voltamperes excitation of the single-phase induction motor must be the same as of the same motor on polyphase circuit, it follows that by operating a quarter-phase motor from single-phase circuit on one primary coil, its primary excit- ing admittance is doubled. Operating a three-phase motor single-phase on one circuit its primary exciting admittance is trebled. The self-inductive primary impedance is the same single-phase as polyphase, but the secondary impe- dance reduced to the primary is lowered, since in single- phase operation all secondary circuits correspond to the one primary circuit used. Thus the secondary impedance in a quarter-phase motor running single-phase is reduced to one-half, in a three-phase motor running single-phase re- duced to one-third. In consequence thereof the slip of s…
The frequency at the wave length lWo is zero, since at this wave length the phenomenon ceases to be oscillatory ; that is, due to the energy losses in the circuit, by the effective resistance r and effective conductance g, the frequency / of the wave is reduced below the value corresponding to the wave length lw, the more, the greater the wave length, until at the wave length lWo the frequency becomes zero and the phenomenon thereby non-oscillatory. This means that with increasing wave length the velocity of propagation of the phenomenon decreases, and becomes zero at wave length lWo.
60. As more fully discussed in the chapters on the single-phase induction motor, in ” Theoretical Elements of Electrical Engineer- ing” and ” Theory and Calculation of Alternating-current Phenomena,” the single-phase induction motor has inherently, no torque at standstill, that is, when used without special device to produce such torque by converting the motor into an unsym- metrical ployphase motor, etc. The magnetic flux at standstill is a single-phase alternating flux of constant direction, and the line of polarization of the armature or secondary currents, that is, the resultant m.m.f. of the armature currents, coincides with the axis of magnetic flux impressed by the primary circuit. When revolving, however, even at low speeds, torque appears in the single-phase induction motor, due to the axis of armature polarization being shifted against the axis of primary impressed magnetic flux, by the rotatio…
Since the resultant m.m.f. of the machine, which produces the flux, is the difference of the field excitation. Fig. 2 ID and the armature reaction, then if the armature reaction shows an initial os- cillation, in Fig. 21 E, the field-exciting current must give the same oscillation, since its m.m.f. minus the armature reaction gives the resultant field excitation corresponding to flux $. The starting transient of the polyphase armature reaction thus appears in the j&eld current, as shown in Fig. 22C, as an oscillation of full machine frequency. As the mutual induction between armature and field circuit is not perfect, the transient pulsation of armature reaction appears with reduced amplitude in the field current, and this reduction is the greater, the poorer the mutual inductance, that is, the more distant the field winding is from the armature wind- ing. In Fig. 22(7 a damping of 20 per cent is assumed,…
On the field current, which, due to the single-phase armature reaction, shows a permanent double-frequency pulsation, is now superimposed the transient full-frequency pulsation resultant from the transient armature reaction, as discussed in paragraph 20. Every second peak of the permanent double-frequency pulsation then coincides with a peak of the transient full-frequency pulsa- tion, and is thereby increased, while the intermediate peak of the double-frequency pulsation coincides with a minimum of the full- frequency pulsation, and is thereby reduced. The result is that successive waves of the double-frequency pulsation of the field current are unequal in amplitude, and high and low peaks alter- nate. The difference between successive double-frequency waves is a maximum in the beginning, and gradually decreases, due to the decrease of the transient full-frequency pulsation, and finally the double-frequ…
216. The main causes of a pulsation of reactance are : magnetic saturation and hysteresis, and synchronous motion. Since in an ironclad magnetic circuit the magnetism is not proportional to the M.M.F., the wave of magnetism and thus the wave of E.M.F. will differ from the wave of cur- rent. As far as this distortion is due to the variation of permeability, the distortion is symmetrical and the wave of induced E.M.F. represents no power. The distortion caused by hysteresis, or the lag of the magnetism behind the M.M.F., causes an unsymmetrical distortion of the wave which makes the wave of induced E.M.F. differ by more than 90° from the current wave and thereby represents power, - the power consumed by hysteresis.
237. The main causes of a pulsation of reactance are : magnetic saturation and hysteresis, and synchronous motion. Since in an ironclad magnetic circuit the magnetism is not proportional to the M.M.F., the wave of magnetism and thus the wave of E.M.F. will differ from the wave of cur- rent. As far as this distortion is due to the variation of permeability, the distortion is symmetrical and the wave of induced E.M.F. ‘represents no power. The distortion caused by hysteresis, or the lag of the magnetism behind the M.M.F., causes an unsymmetrical distortion of the wave which makes the wave of induced E.M.F. differ by more than 90° from the current wave and thereby represents power, - the power consumed by hysteresis.
I of the synchronous machine, corresponding to the field excita- tion. The actual magnetic flux of the machine, however, does not correspond to e, and thus to the field excitation, but corre- sponds to the resultant m.m.f. of field excitation and armature reaction, which latter varies in intensity and in phase during the oscillation of 0. Hence, while e is constant, the magnetic flux is not constant, but pulsates with the oscillations of the machine. This pulsation of the magnetic flux lags l>ehind the pulsation of m.m.f., and thereby gives rise to a term in 6 in equation (28). If PB, &, e, eu, Z are such that a retardation of the motor increases the magnetizing, or decreases the demagnetising force of the armature reaction, a negative term, P,, appears, otherwise a positive term. Pi in this case is the energy consumed by the magnetic cycle uf the machine at full frequency, assuming the cycle at full fre…
Assume now that a ground, P, is brought near one of the IjneBi A, to within the striking distance of the voltage, e. A dischaigB then occurs over the conductor, P. Such may occur by the puiu>* ture of a line insulator as not infrequently the case. Let r «■ re- sistance of discharge path, P. While without this discharge path, the voltage between A and C would be ei = e (assuming sini^ phase circuit) with a grounded conductor, P, approaching line A within striking distance of voltage, e, a discharge occurs over P forming an arc, and the circuit of the impressed voltage, 2 s, now comprises the condenser, C2, in series to the multiple circuit of con- denser, Ci, and arc, P, and the condenser, Ci, rapidly discharges^ voltage, eij decreases, and the voltage, 62, increases. With a de- crease of voltage, ei, the discharge current, i, also decreaseSi and the voltage consumed by the discharge arc, e’, increases un…
For instance, if in an isolated high-potential transmission line, the ground is brought within striking distance of one of the line conductors - as by the puncture of an insulator. A spark dis- charge then occurs to the ground, and the arc following the spark discharges the line by a transient oscillation, that is, brings it down to ground potential (and the other two lines, in a three- phase sj^stem, then correspondingly rise in voltage to ground, from the Y to the delta voltage). As soon as the line is dis- charged the arc ceases, that is, the spark gap to ground opens, and the line then charges again, from the power supply of the system, and its voltage to ground rises, until sufficient to jump to ground again and start a second transient oscillation, and so on continual transient oscillations follow each other, as a ^‘con- tinual transient,” or ”arcing ground.” Oscillograms, Figs. 59 and 60, show su…