Synchronous Generator

The theory of the synchronous machine is well known, so only the basic model characteristics will be described here. A cross sectional view of a 3-phase, 2-pole, salient-pole synchronous machine is shown in Fig. SM-1. The stator phases are represented by three sinusoidally distributed windings, displaced by 120 degrees. The rotor contains one field winding (fd) (shown under the poles of the rotor), one damper winding in the same magnetic axis as the field (kd) (shown at the center of the rotor), and two damper windings in an axis ahead of the magnetic axis of the field (kq1 and kq2) (shown in the polefaces). The damper windings are short circuited windings which represent paths for induced rotor currents. Since most synchronous machines are operated as generators, it is assumed that positive stator current flows out of the machine. Therein positive electromagnetic torque corresponds to generator operation and negative electromagnetic torque corresponds to motor operation. From Fig. SM-1, it can be seen that the self-inductances of the stator windings as well as the mutual inductances between the stator and rotor windings are functions of the rotor angular position. In the model used herein, Park’s transformation is applied to the stator variables (voltage, current, flux linkage), which replaces the variables associated with the stator windings with variables associated with fictitious windings that rotate with the rotor. This change of variables has the effect of eliminating the angular position-dependence of the inductances.

Fig. Sm-1: Cross-sectional view of a two-pole, salient-rotor, three-phase synchronous machine

The change of variables which constitutes Park’s transformation may be expressed symbolically as

where

and f may be voltage, current, or flux linkage.

For state-variable based simulation, the equations of the synchronous machine are conveniently modeled by expressing the flux linkages per second (state variables) in terms of the voltages applied to the machine.

where the superscript r represents that the equations are transformed to the rotor frame of reference. The subscript “s” indicates stator quantities. The rotor voltage equations are not transformed; however, they are expressed in terms of the transformed stator variables. In particular,
It is assumed that rotor variables are referred to stator windings by the appropriate turns ratio [10]

The quadrature and direct magnetizing flux linkages are expressed as

The expressions for the stator (in rotor reference frame) and rotor currents can be found using equations SM-14 to SM-20

Equations SM-4 to SM-20 provide electrical quantities of the machine. The synchronous machine is an electromechanical device, and thus also requires expressions for the electromagnetic torque and the speed of the machine. Equation SM-21 expresses the electromagnetic torque in terms of the flux linkages, and equation SM-22 determine the rotational speed from the electromagnetic torque, load torque, and moment of inertia. In both equations, P represents the number of poles. It should be noted that the model neglects core loss as well as friction and windage loss.

It is often convenient for analysis and physical interpretation to relate the position of the rotor of a synchronous machine to a voltage or the rotor of another machine. In this model, the rotor angle is referenced to the maximum positive value of the fundamental component of the terminal voltage of phase a. The change in rotor angle is expressed in terms of the rotor angular velocity and the electrical angular velocity of the phase voltages as
For constant electrical angular velocity, the rotor angle can be used in relating the torque and rotor speed

Fig. SM-2 shows the Graphic Modeller simulation of the synchronous machine. As noted above, the model for the synchronous machine requires voltages as inputs. Thus one block consists of a three-phase source that provides a balanced set of three-phase voltages. The synchronous machine block is a compound block that contains another level, and will be described in the next paragraph. The final block in the model is the mechanical torque applied to the shaft of the synchronous machine. In the model developed, currents were assumed positive out of the machine, indicating positive torque for generator operation, negative torque for motor operation. The mechanical torque represents an input torque for generator operation and a load torque for motor operation. For convenience there are also two strip plot recorders that plot the stator phase currents and rotor angle. Double clicking them, after a simulation run, will plot the respective variables.

Fig. SM-2: Graphic Modeller simulation of the synchronous machine

Double clicking on the synchronous machine block reveals the next level of detail as shown in Fig. SM-3. Compound blocks can be used to allow multiple levels in a model. In this model compound blocks were used so the model could be used as a tool for undergraudates who are not concerned with the simulation equations. More advanced undergraduate and graduate students, on the other hand can go down a level to understand the theory behind the simulation.

Fig. SM-3: Details of compound block representing the synchronous machine

Since the machine model is based on Park’s equivalent circuits, the input phase voltages and ouput currents must be transformed to and from the rotor reference frame, respectively. Thus the leftmost green block contains the equations to transform the phase voltages to the rotor reference frame, and the q-d-0 rotor reference frame currents to phase currents. The center red block contains ACSL code representing equations SM-4 to SM-21, and is thus the actual simulation of the electrical portion of the synchronous machine. This block also contains constants for the parameters of the machine, which can be changed by the user to represent other machines. The yellow box contains the code for equations SM-22 to SM-24 and determines the speed and rotor angle as a function of time.

The model of the synchronous machine is versatile and can be used to support lectures, laboratory experiments, and homework assignments. One example where the model provides an excellent accessory to education is in explaining various operating characteristics of the machine. Several texts, particularly in power system analysis, develop analytical methods to approximate the transient dynamic characteristics of the synchronous machine. These include developing transient torque-angle curves along with determining transient stability using analytical tools such as the equal area criteria. Although useful, these analytical techniques require approximations which lead to significant inaccuracies and do not account for actual machine behavior. In contrast, using the detailed synchronous machine model to explain the dynamics, a more complete behavior of the system is obtained, without requiring any increase in student prerequisite knowledge.

For example, Fig. SM-4 shows a detailed dynamic response of a 835 MVA steam turbine generator to a 3-phase fault at the stator terminals of the machine. Initially, the machine is operated at 50% of rated conditions (Ti = 1.11e+6 Nm, Exfd = 52 kV). With the machine operating in steady state, a 3-phase fault is simulated by setting the phase voltages to zero at t = 6.0 sec. The fault is then removed by reapplying the voltages at t = 6.2 sec. From Fig. SM-4 it is seen that the fault causes an immediate offset in the stator phase currents, represented by Ibs. This offset is present because flux contained in the machine cannot change instantaneously; therefore, a dc offset in the phase currents occurs to maintain the flux at pre-fault values. The dc offset in phase currents is reflected as oscillations in the transformed stator currents and the electromagnetic torque. Most undergraduate students will not have knowledge of Park’s transformation, or the respective transformed variables; however the compound blocks provide a means to remove that level of detail. In this example, the initial swing of the electromagnetic torque causes the rotor to decelerate. This, in turn, causes the rotor angle to decrease, in what is commonly referred to as a ‘back swing’. Back swings are not accounted for in analytical methods of analysis, and are a source of error in approximating transient dynamic behavior. Because the phase voltages are zero, the machine has no means of transmitting power to the system, and therefore the rotor begins to accelerate. The rotor continues to accelerate until the fault is cleared by reapplying the phase voltages. Upon reapplication of the phase voltages (clearing of the fault), initial offsets in the phase currents appear and again produce 60 Hz oscillations in the rotor reference variables and the electromagnetic torque.

Fig. SM-4: Results of application and removal of a three-phase short circuit

In this particular example, the machine eventually returns to the inital pre-fault operating point, as demonstrated by the plot of the power angle, delta. Repeated fault simulations can be used to determine the critical clearing time, and to demonstrate the inability of the system to obtain pre-fault operating conditions once the critical clearing time is exceeded.

The results of a fault-study in which the fault is cleared after the critical clearing time are shown in Fig. SM-5. In this case the rotor angle settles to a steady-state, post-fault value of approximately 390 degrees. In other words, the rotor has advanced a complete revolution ahead of the system (which is referred to as slipping a pole). Because of the large torques that occur on the turbine-generator during pole slipping, synchronous machines in the United States are designed with protection to prevent its occurance.

Smf41.jpg (29598 bytes)
Fig. SM-5: Results of application and removal (after the critical clearing time) of a three-phase short circuit

For graduate and more advanced undergraduate students, the linear menu in the ACSL command window provides the user with a host of analysis options. Included are options to compute the Jacobian, a linearized system model, the eigenvalues of the system, as well as bode, nyquist, and root-locus plots. These options provide a means to test various control techniques, evaluate operating conditions, determine input/output impedances, and explain system behavior in more detail. In the synchronous machine stability example described above, the eigenvalues of the system were computed within ACSL at steady state and are shown in Table SM-1. Using these, the system behavior can be explained in linear system-theory detail. In particular, the complex set of eigenvalues with imaginary components approximately equal to the base frequency of the system correspond to the transient stator currents that produce 60 Hz oscillations in the electromagnetic torque. This complex pair is often referred to as the stator eigenvalues. The low frequency complex pair corresponds to the principal mode of oscillation of the rotor relative to the electrical angular velocity of the system and are portrayed in the damping and long-term oscillatory behavior observed in the rotor velocity and angle. The remaining eigenvalues are real and correspond to the rate of decay of the transient currents in the rotor electrical windings.

Table SM-1: Complex eigenvalues of a large synchronous machine, in ascending order, computed by ACSL
Eigenvalue REAL IMAGINARY FREQUENCY DAMPING
1 -0.37690500


2 -0.98638200


3 -5.95093000


4 -1.94917000 +/-9.69484000 9.888840 0.197108
6 -10.2192000


7 -53.7368000


8 -4.44606000 +/-376.957000 376.984


The model is compatible with machines of all ratings. Therefore it can be used in a laboratory environment to demonstrate the expected behavior of actual machines the students are using. In addition the dynamic performance of various types of machines can be easily compared and the differences explained. For example, a small horsepower synchronous machine will have a significant difference in dynamic performance compared to a large-scale generator. This is well illustrated by comparing the fault responses of the 835 MVA generator depicted in Fig.-SM4 with the fault response of a 5-HP machine used in the Emerson Electric Machines Laboratory at Missouri-Rolla. The 5-HP machine is a 220 volt, three-phase, two-pole generator. The response of the machine, initially operating at Ti = 8.0 Nm and Exfd = 200 V, to a three-phase fault at the stator terminals is shown in Fig. SM-6. Comparing Fig. SM-4 and SM-6, it is clear the 5-HP machine exhibits a much more damped response. In particular, the stator currents and electromagnetic torque exhibit a much more damped response and they do not contain the sustained 60 Hz oscillations exhibited by the large machine. This is due to the fact that the rotor circuits of the 5HP machine have much larger resistance values than those of the turbine-generator. Therefore, the rotor circuits have much shorter time constants, and the flux in the 5 HP machine can change much faster than the turbine-generator. Since the flux can change faster, the DC offset in the stator variables is very short lived. Thus the 60 HZ oscillations in the torque and the transformed stator variables are barely observed. The difference in responses can also be explained by comparing the eigenvalues of the respective machines. The eigenvalues of the 5-HP generator are shown in Table-SM-2.
http://ewh.ieee.org/soc/es/Nov1998/08/FIGURES/SMF6A.JPG
Fig. SM-6: Short Circuit Response of a 5-HP Laboratory Generator

Synchronous Motors

A synchronous motor can be defined as being, merely, an alternator used as a motor. The transmission of power between an A.C. generator and an A.C. motor is, therefore, nothing more than a particular case of the coupling of two alternators in synchronous operation. Indeed, it is precisely through the study of the features of the coupling of alternators in parallel that the occasion presented itself of noting the phenomenon of the reversibility of alternators, that is to say, the possibility of using the same machine both as a motor and a generator, provided that it shall have been previously brought to a speed absolutely equal to that of the generator which supplies it with current.

We can easily understand the possibility of operating such a motor by comparing it to a motor with commutated current. It is known that if the current of a shuttle armature of the Siemens ("H") type is commutated at each half revolution, the motor-couple is always in the same direction when the machine is supplied by direct current. In an A.C. system, the same result is obtained without a commutator, because the direction of the supply-current changes at each half revolution, and this effect occurs only when the motion of the motor is synchronous, that is to say when the armature advances the distance of one pole during one alternation of the supply-current.

Although this property was noted as early as 1869 by Wilde, it passed unnoticed during more than ten years, and it has really been known only since the experiments of J. Hopkinson and Grylls-Adams, at the South Foreland Lighthouse, in 1883. The Memoir of Hopkinson (in which, without knowing the work of Wilde, he gives the explanation to which reference will be made later) , was epoch-making in the history of alternating currents.

In the South Foreland experiments, the alternators used were three similar de Meritens singlephase alternating current machines, all belt-driven from a common source of power. These machines could be easily coupled in parallel, as generators, by bringing them to the same speed before coupling them. The belt being then removed from one of them, it was observed that it continued to run synchronously by the action of the current of its neighbors, and that it could even develop a considerable amount of power, as measured by a friction brake, before losing its synchronism. These experiments were repeated a few years later by Mordey, on a much larger scale, with machines of low inductance presenting a much greater stability of operation and driven by independent prime movers. He was thus able to demonstrate the synchronizing power of the alternators on the motors or engines driving them, and even to cause one of the latter, with the power shut off, to be dragged by one of the alternators which it was driving. This gives the key to the principles involved in parallel working. He also showed, later, the possibility of accomplishing this coupling with machines connected by means of long lines of high resistance.

Synchronous Motors and Alternators

Synchronous motors have the same construction as alternators. The few special features relative to the production of the direct current necessary for their excitation will be treated separately, later. It will be assumed that the reader is already familiar with the general details of construction of alternators.

There are motors having movable armatures and stationary fields, or vice versa, and also motors with revolving iron masses in which all the windings are stationary. These machines are similar to the generators of the same types; for example, Fig. 1 indicates, diagrammatically, the principle of construction of a two-phase synchronous motor, with a ring armature and movable fields, receiving an exciting current through the brushes b1 and b2 .

These motors are designed like generators, the essential condition to be fulfilled being to have a low armature-reaction and powerful inducing fields, in order to obtain good stability.

Number of Poles

Although it is more difficult to increase the number of poles for small powers than for large powers, the construction of small synchronous motors for ordinary frequencies (40 to 60 cycles) presents no special difficulties, if the speeds corresponding to these frequencies are not objectionable, because these speeds are perfectly allowable so far as centrifugal force is concerned.

Synchronous Motors at low Speeds

On the other hand, in the construction of small synchronous motors to run at low angular velocities, it is extremely difficult to find space for the numerous conductors and for the exciting or field coils, which must produce as many ampere-turns as in the case of large motors. For this reason non-synchronous motors are more convenient for low rotative speeds.

The author has been able, however, to produce motors of low power (a few hundred watts) which have moving iron and have a very high number of poles (as many as 50 for example), by utilizing inductiontype excitation, the magnetic circuit being closed exteriorly, as shown in Fig. 2, in such a way as to allow all the space needed for the exciting coils.

These coils can then be replaced by permanent magnets, thus producing motors which run without excitation, at speeds sufficiently low to be synchronized by hand, and which can render useful service, in certain applications, such as for oscillographs. For this purpose the author preferably employs a small horseshoe magnet that is made to revolve around a stationary armature having a number of poles which is a multiple of 6. It is possible, in this way, to obtain very stable synchronous rotation of a revolving mirror without expending more than 1.5 to 2 watts.

Several firms made a specialty of synchronous motors, at an early date, among which we may mention La Societe 1'Eclairage Electrique in France, and the Fort Wayne Company in America.

One form of motor constructed in France by the Societe 1'Eclairage Electrique (Figs. 3 and 4), is constructed for polyphase currents or for single-phase currents, for powers ranging from 1 to 130 H.P. Table 1 gives the principal data referring to these matters.


Efficiency Synchronous Motors

The efficiencies of the three-phase motors are a little higher than those given for the single-phase motors. The horse-powers given in this table correspond to a frequency of 42 periods, but these motors can be also used at frequencies between 40 and 60 periods, and their power then increases with the frequency.

As table 1 shows, types Nos. 14 to 30 are made with 4 poles, self-exciting. For higher powers, the number of poles increases, and the excitation is obtained by means of a small direct current exciter mounted on the same base. Above type 90 the armature is stationary and the fields turn inside. The fields are of mild cast steel, the armatures being slotted.

As an example of these large motors may be cited several from 50 to 100 H.P., giving the best of results on the power-transmission system around Grenoble, notably at Voiron, a distance of 30 kilometers from the generating station. Their efficiency is from 90 to 92 per cent. One of these motors even works in parallel with a steam-engine of the same power, and it compensates for the variation of angular velocity of the engine as it passes the dead centers.

All these motors are provided with a clutch and with an idle pulley for starting, as will be explained later. When running, they can undergo considerable variations of load without falling out of step.

Attention should also be called to another interesting type of synchronous motor, the Maurice Leblanc type, which is characterized by the addition of closed circuits in the pole-pieces to insure a perfect damping of oscillations, as will be seen later.


Case of Equal Electromotive Forces

Let us suppose that the electromotive forces of the generator and motor are equal, and, to simplify matters, let us take, as generator and motor, two machines whose excitations are regulated to approximately the same value. Let the two machines be driven by belts (Fig. 5) ; and, when they have attained the same speed, let them be coupled together (experiment of Hopkinson and Grylls-Adams). Let us, moreover, make use of an apparatus of the kind described in Chapter VII, whereby the difference of phase between the two machines may be determained.

It will be noted, in the first place, that as soon as the two machines are brought to the same speed, the current which passes from the one to the other practically disappears. Moreover, the "phases are identical," i.e., the poles of like polarity pass at the same time in front of the corresponding portions of the two armatures.

The induced E.M.F. Synchronous Motor

The induced E.M.F.'s between the corresponding terminals a, b, and A, B, are therefore in unison. If we measure them, on the contrary, in the direction in which they appear, by following the circuit ab, BA, it will be found that they are exactly opposed to each other.

Let us now suppose the belt of one of the two machines to be removed. This machine will continue to turn at the same speed, but it gives indication of a certain very slight delay or falling behind, technically termed "lag" with respect to the other machine. Moreover, the current in the circuit now becomes appreciable.


Stalling of a synchronous motor

If a brake be placed on the pulley and if the load be gradually increased in such a way as to increase the mechanical power produced by the motor, the "lag" of the motor will be seen to increase at the same time as the current.

When this lag approaches a quarter of a period, i.e., half an interpolar space, the machine slows up all at once and stops as if held fast by the brake. We then say that it is "stalled," or " out of synchronism", or "out of step." The current in the circuit rises to a very high value as soon as the machine falls out of synchronism; and it becomes approximately equal to the short-circuit current in the circuit when the machine is stopped. In order to avoid accidents, it is necessary to introduce fuses in the circuit, or to provide some automatic disconnecting device, which will prevent the excessive load.

It is seen that what characterizes the synchronous motor is the increase of phase-lag with the load and the "stalling" of the motor or its falling out of step beyond a certain maximum load.

In a good motor, the limiting load should amount to at least 1.5 times, or, better, to twice the normal load. This limit is guaranteed by most makers of synchronous motors.

On the other hand, if the motor is run by a belt in such a way as to give it a "lead in phase" with respect to the machine or the circuit which supplies it with current, it can be found, by wattmeter measurements, that this power changes in sign, i.e., the motor acts as a brake and returns energy to the circuit instead of receiving it therefrom.

The phenomena become more complicated still on varying the E.M.F. of the motor or of the generator.

Case of Unequal Electromotive Forces

An interesting and characteristic property of synchronous alternating current motors, and which distinguishes them absolutely from direct current motors or from alternating current motors having commutators, is that they can be excited so as to give a voltage greater than that of the supply-circuit. For example, it is possible to feed, from a no-volt circuit, a motor which, driven by belt at the same speed, produces an E.M.F. of 120 to 150 volts at its terminals. But, if the E.M.F.'s are thus unequal, the current passing between the generator and the motor, when the latter is running without load, can, instead of being inappreciable, attain a considerable value.

Likewise, when the motor is running with load, the current is greater than that which corresponds to the work to be done. The same effects are produced when, instead of giving to the motor an excessive excitation, it is given an insufficient induced E.M.F. It is then observed, if the machines are alike, that the potential difference at the terminals assumes a third value, which is the mean of the two E.M.F.'s involved.

In both cases, the greater the inequality between the two E.M.F.'s the more the current measured will increase, by the change of excitation. If we plot a diagram, taking, as abscissae, the values of the excitation of one of the machines, and, as ordinates, the current passing through the circuit, the curve of variation of the latter, as a function of the former, has the form of a V more or less rounded at the bottom (Fig. 6). This form persists, although it may be less marked, when a constant load is placed on the brake. At the same time that the current increases, by reason of an inequality of the E.M.F.'s, it can be noted, by means of an apparatus for indicating phase-difference, that the current undergoes a change of phase, either forward or backward, with respect to the E.M.F. of the motor. This can be expressed in another way by saying that the machine consumes or produces wattless current, i.e., current which is "out of phase" being pi/2 behind or ahead of the E.M.F. This "wattless" current, which has the effect of increasing the "apparent" current, is thus named because it produces no work, the load on the brake remaining constant, by hypothesis.


Equations of Synchronous Motors; Analytical Theory

We have just examined the phenomena of synchronous motors from a physical point of view. We shall now represent them analytically, according to the theory first expounded by Dr. J. Hopkinson, but with a few modifications in form. We shall suppose with him that the E.M.F.'s and currents follow the sinusoidal law, and that the reactances of the machine are constant.

Let us suppose, then, a single-phase A.C. generator and motor, defined by their induced E.M.F.'s, their resistances, and their mean inductances, which are all supposed constant.

Let:
  • T=the duration of the period;
  • ω=/T =the speed of pulsation of the currents;
  • e1 and e2 = the instantaneous values of the generator and motor E.M.F.'s respectively, at the instant t;
  • E1 and E2 = the effective values equal to the amplitudes of the sinefunctions, i.e., the maximum value, divided by √2;
  • t0/T = the phase-difference between e1 and e2;
  • Θ = the angle of lag (phase-difference) corresponding to Θ=2πt0/T;
  • R and L = the resistance and inductance, respectively, of the total circuit, of the two machines;

  • i= the instantaneous value of the current;
  • I = the effective value of the current, equal to the maximum value divided by √2.

Let us suppose the conditions of stability to be unknown and let us seek to ascertain how two alternators connected in series will operate. The two sine-functions of the E.M.F. represented by the curves e1 and e2 in Fig. 11, may be formulated by the equations,

In which Θ designates the angular distance between the actual position of e1 and the position of opposition of e2.


Equations of Synchronous Motors; Analytical Theory

The E.M.F. which is acting in the circuit is equal to the algebraical sum of the opposing E.M.F.'s.

From this the current, i, may be deduced, by the well-known differential equation,

In this equation let i=X sin ωt+Y cos(ωt).

If this value be substituted in the equation, the values of X and Y can be determined by making the coefficients of the sine-terms and of the cosine-terms successively equal to zero. We can then obtain, by differentiation, substitution, etc., the following value for i:

This may also be written,

In this equation β=the phase-angle of the resultant E.M.F. and γ=the supplemental phase-difference of the current measured from this E.M.F. In the simple particular case where E1 = E2

this expression reduces to


or, since

we will have

i.e., the current will have the effective value

and will be out of phase by the angle γ with respect to the resultant E.M.F., which is itself out of phase with respect to the mean of e1 and e2. This result is easily interpreted in Fig. 11, by drawing the resultant curve e1 + e2 obtained by taking the difference of the ordinates of the first two curves. It will be seen that the curve has actually a phase-difference equal to with regard to π/2 the mean of e1 and e2, and that it increases with the phase-difference of e2 with respect to e1. In consequence of the lag, γ, of the current, measured with respect to this re.sultant E.M.F. (when γ is near π/2 in value), it will be seen that the current is approximately in phase with this mean value; it would be completely so if there were no resistance-losses.

The power-outputs of the two machines will be obtained by multiplying the instantaneous current i by the E.M.F.'s. e1 and e2. For example, in the case where E1 =E2 , we have


Likewise, on multiplying by -e2, we will have

These equations show that the power is not constant, in either case, but pulsating, i.e., it presents variations of frequency= 2 T, as represented in Fig. 11.

These variations constitute sine-functions having pulsations twice as rapid as those of the current, which have for their axes the horizontal lines (P1, P2) corresponding to the mean powers given by the first terms within the brackets in the following equations:

The very small difference between P1 and P2 represents the loss by resistance (Joule effect). The axis of the curve P1 is therefore a little more above the axis of zero power than the axis of symmetry of the curve P2 is below it.

The torque could be obtained, in each case, by dividing the power by the angular velocity. These expressions show that the current increases with Θ until Θ equals π, but the torques, which equal zero so long as the lag Θ=zero, increase with Θ only until the value Θ = γ; and they then decrease.

Stability will, therefore, exist only with Θ < γ having for its axis the exact opposition of E.M.F.'s.

The solution, in the case where E1 is different from E2, will be obtained in an analogous manner, by forming the products e1i - e2i; and it would still give pulsating values for p1 and p2 ; but, since these caculations are uselessly complicated, we will pass them by and turn to more simple methods.


Synchronism

In proportion as the armature-speed increases, the magnetic pulsations produced by it in the pole-pieces become less numerous, as can be seen on connecting a lamp to the field-circuit and noting its variations of brightness. It is well to provide a centrifugal regulator which connects this lamp in circuit only when the speed approaches synchronism, because, at lower speeds, it would be subjected to excessive voltage. When synchronism is almost attained (the speed generally remains slightly lower,) the fields are excited when the phases come into opposition, the motor falls into step, and the current immediately diminishes, owing to the disappearance of the reactive current which was absorbed up to that time. The more carefully the time has been selected for closing the excitation-circuit, the more easily the motor will fall into step. It is well, as a rule, to include, in the circuit, a variable self-inductance, which has the effect of preventing excess of current and of damping objectionable harmonics.

When once the motor is in synchronism, it can be loaded progressively, by shifting the belt from the idler to the driving pulley.