Chapter 38. Synchronous Generators—Alternators – Electrical Technology, Vol2: Machines and Measurements, 1/e


Synchronous Generators — Alternators


In this chapter you will learn about:

  • The difference between d.c. generators and alternators
  • The physical construction of a.c. machines
  • Slot structure in a.c. dynamos
  • Coil and pole group connections
  • Stator windings
  • Pitch factor and distribution factor
  • Alternator performance at various load power factors
  • Voltage regulation of an alternator at various power factors
  • Winding resistance and synchronous impedance
  • Equivalent circuit of a synchronous alternator
  • Basic voltage generation formula
  • Requirements for parallel operation of alternators
  • How to meet these requirements
  • Different methods of synchronization

Slot structure in alternators


Alternating current dynamos are visually different from d.c. machines of comparable sizes. The difference in appearance has a fundamental basis because the machines are inside out in relation to d.c. machines. Most a.c. machines have the armature in the field or stator position and the field in the moving or rotor position. This arrangement is the natural order of things for a few very good reasons (see Figure 38.1).

  1. The high voltage, high current and, therefore, high power-handling element is the armature on any a.c. or d.c. rotating electrical machine. Armatures coils are, therefore, larger than field coils.
  2. Since no alternate switching of coil polarities is needed on an a.c. machine, no commutator function is needed. Thus, the high-power windings may be made stationary for direct connection. The universal motor is an exception to this condition.
  3. The field structure and coils are not ordinarily required to handle more than a fraction of the total power. Thus, their rotating electrical connection may be made smaller. Since no polarity switching is required, collect rings are usually used.
  4. The armature and field coils are both placed in slots in the punched magnetic structure, but the stationary armature structures can be conveniently made with deeper slots to handle the required larger coils.
  5. It is easier to cool the stator than the rotor, which is an advantage of the normal a.c. construction.

Figure 38.1 A Cylindrical Rotor


Except for specialized types, such as the universal a.c. - d.c. motor, which appears much like a d.c. series motor, almost all a.c. motors and generators are built to take advantage of the natural relation of having the armature fixed and surrounding the field and the field moving and inside of the armature.

38.2.1  Fixed Armature or Stator

The fixed and outside armature has a complete ring of teeth and slots on its inner face. In the usual machine, all the slots are filled with similar and symmetrical coils. As a result, it may not be at all obvious how many poles or phases are present in the winding. In the field rotor, the constructions may be much like that of a d.c. armature with a complete circular magnetic structure having a continuous group of slots and teeth on the outer surface. Again, these slots are filled with similar and symmetrical coils and it is not readily apparent how many poles or phases are present in the machine. With salient pole field construction, the number of poles is visible, as in a d.c. machine. A salient pole machine is illustrated in Figure 38.2.

Figure 38.2 A Salient Pole Machine

If the winding slot sides are parallel to each other in a single slot,

which is a frequent construction, it may be seen from Figure 38.3 that the stator tooth structure becomes stronger as it grows deeper. On the other hand, Figure 38.3 shows that a rotor tooth becomes weaker as it grows deeper. This tooth structure advantage for the stator is used in the a.c. stator.

Figure 38.3 Typical Magnetic Lamination Slot Structure in an a.c. Dynamo

Parallel side slots are not necessary in small sizes. However, on large sizes, where the coils are wound with large cross-sectional wire and where the insulation must be most carefully distributed, the parallel side slot is required. Since large coils are preformed, bound with insulation and impregnated with varnish and baked, they cannot readily change shape after installation in the magnetic coil.

Smaller a.c. machines are wound with loose coils of round wire, which may be slipped down into the slot turn by turn during winding or installation. In this fashion, almost any slot shape may be used. Full use of the slot cross-section secures to require parallel side slots in larger sizes. In any shaped slot, some provision must be made to capture and hold the windings in place. As a result, the slot will have some provision for a covering wedge, even if parallel sided.

In the a.c. machine stator, the current is continually varying at the frequency repetition rate. The resulting magnetic flux then varies cyclically, and there are hysteresis and eddy current losses in the magnetic structure. Minimizing these losses requires the use of a laminated magnetic structure. The structure is built up of thin plates of silicon steel alloy that are readily punched to shape in press dies built for the task. The punched stator laminations usually cover full circle in small- and-medium sized machines. Since punch dies are expensive, only a few different numbers of slots and teeth are provided for a basic size.

The larger-sized machines are built up with laminations in segments of reasonable sizes. The size depends on the available stock width and press die size.

Lamination stock thickness is dictated by eddy current loss considerations. Thin lamination has less eddy current loss but becomes difficult to handle and the teeth will bend too easily. A stock thickness of about 0.35 mm has long been used for 60 Hz a.c. machines.

The numbers of slots are standardized around 36, 48, 60 and 72 slots, and so on, for good mechanical reasons. These will become more apparent when actual windings are discussed.

38.2.2  Rotating Field Structure

The mechanical construction of the rest of an a.c. motor or generator follows closely that for d.c. machines except for the lack of a commutator with synchronous alternators and synchronous motors, slip rings—which are used to carry d.c. power into and out of rotating field—are used in a similar location to a commutator.

A slip ring as illustrated in Figure 38.4 is a copper alloy ring that is insulated from the rotor shaft and connected to the rotor windings. A carbon brush is supported in a brush carrier rigging to complete the connection. Since there is no requirement for a particular internal resistance to aid commutation, the slip ring brush is harder and denser than a commutator brush. It has a lower voltage drop and is therefore responsible for less power loss than its d.c. counterpart.

Figure 38.4 In an a.c. Generator the Rotating Conductor is Connected to the Load Through the Slip Rings and Brushes (a) Electrical Parts of an a.c. Generator (b) Simplified Sketch of the Conductor Loop

When the rotor windings carry three-phase a.c. power, three slip rings are used. In some cases regarding larger synchronous motors, multiple windings are used and five or mover slip rings may be present.

The high-power armature windings are placed on the stator structure, which has relatively larger winding space. Overall, an a.c. machine can usually be smaller than its d.c. counterpart with the same power rating. The lack of a commutator also contributes to size reduction. An a.c. machine averages about 50 per cent more power within the same frame size.


The types of windings used in a.c. machinery are closely related to d.c. windings. Both lap and wave windings are used, but lap winding is much more common owing to shorter coil connections. In single phase machines, a winding form called concentric coils is used not because of any circuit advantage, but because it lends itself to prepared coil structure that can be put in place rapidly. Here the economics of construction dominate.

Since three-phase machines require three identical groups of windings spaced 120 electrical degrees apart, and since poles must exist in pairs, certain rules affect windings and magnetic structure slot spacing.

Electrical degrees refer to the cycle angle of the repeating sine wave, where one full cycle is 360 electrical degrees. Since opposite magnetic poles produce opposite voltages in a moving coil to pole situation, the maximum voltage difference along a sine wave is found 180 electrical degrees apart. This 180 electrical degrees shift takes place between each successive field pole. The total electrical degrees in a 360 mechanical degree (Figure 38.5) rotation is then simply 180 times the number of poles or the


total electrical degrees in one revolution = 180 P


where, P is the number of poles.

For example, take a three-phase four-pole machine. Let us assume that 36 slots are available in the stator lamination stock. There are 36/4 = 9 slots per pole position and 9/3 = 3 slots per phase per pole. These 36 slots would allow twice as many or six, per phase per pole for a two-pole machine, and similarly, two slots per pole per phase for a six-pole machine.

Figure 38.5 Electrical and Mechanical Degrees (a) Four-pole Magnetic Field (b)720 Electrical Degrees Per Revolution

38.3.1  Chording of Windings

One design factor is the chording of the pole windings. If, on the 36 slot, four-pole machine an individual coil enters slot 1 and comes back from slot 9 (see Figure 38.6); it will have spanned 90 mechanical degrees of the stator circular structure. Since there are four poles by definition, in this case, 90 mechanical degrees is 180 electrical degrees (Eq. 38.1). Thus, the two sides of the coil are in the same relative position on the adjacent north and south pole positions. This is a full-pitch coil construction (see Figure 38.6).

Figure 38.6 Four-pole a.c. Stator with Full Pitch Coils

The more usual a.c. machine coil will cover less of the periphery of the machine and is then said to be fractional pitch. A typical coil situation might have a coil enter slot 1 and leave slot 7.

This then covers six out of a possible nine slot pitches and is a 6/9 or 66.7 per cent pitch. The majority of a.c. machine coils are of fractional pitch type, for which there are a few important advantages.

  1. The ends of the coil are shorter, which means less copper loss due to less total length.
  2. The ends of the coil can be formed more compactly. The end bells will need less winding space, resulting in a shorter unit.
  3. There is a distinct reduction in machine harmonics due to cancellation of higher harmonics. Since all a.c. equipment is designed to operate on a pure sine wave, the generation of harmonics is to be avoided.

38.3.2  Coil Group Connections

Figure 38.7 illustrates the manner in which the coils are laid into the slots. A vast majority of lap or wave-wound machines use this double-layer winding arrangement. This is very similar to the manner of winding a d.c. armature. This interconnection of the coils will result, in this 36-coil situation, in 12 groups of the coils per group. Each group is then involved with one phase and one pole. Since there are four poles in this simple but real situation, there are four coil groups in each phase. This is the usual situation, even when more slots or coils are used.

Figure 38.7 Double-layer Coils in a.c. Stator

A 72-slot, six-pole machine, when wound for three phase, would have 72/6 = 12 slots per pole and 12/3 = 4 slots per phase per pole. Here the coils would be connected in groups of four, and there would be six of these four-coil groups per phase.

Many varieties of coil group connections are possible, but only a relatively few are used today. In a three-phase machine, the coil groups per phase are connected for all the poles, and this larger grouping is usually divided into two parts. On the 36-slot machine, 2 three-coil groups are permanently connected. There are then two of these six coil connections per phase. If they are series connected, then the motor or generator will be set for operation on the higher of its two rated voltages. If parallel connected, the lower of the two rated voltages may be accommodated. In this way, a motor or generator may be operated on either 110 V or 220 V or perhaps 220 V or 440 V and so on. Great installation flexibility is inherently obtained.

As these coil groups are gathered together, the direction of winding or connection on opposite poles must be opposite. Thus, each adjacent series connected per phase per pole group must be reversed for proper polarity, as shown in Figure 38.8 for typical coil interconnection.

A three-phase machine, when gathered into phase coil groups, is then connected either in wye or in delta, and also in series or parallel as shown for wye connections in Figure 38.8. Three-phase motor stator coil group ends are normally numbered from 1 to 9 as shown, and the points 10,11,12, are normally buried unless specially needed.

38.3.3  Winding Distribution

Since coils are usually laid in the manner shown in Figure 38.6, they are seen to be spaced uniformly around the periphery of the machine stator. Returnning to the 36-coil, four-pole situation, it can be seen that in this specific case any one-pole has three phase groups of three series connected coils per pole. The voltages generated in coils of single-phase groups of three coils are not simply additive. Since each coil is not swept or cut by the same intensity of magnetic flux at the same time, they are not in the same time phase relation even though they are a part of the same phase winding. The individual coil voltages must be combined as phasors. All these factors, which make up a multi phase, two level, chorded or whole-pitch distributed winding, are applicable for a variety of a.c. generators and motors, both large and small.

Figure 38.8 Typical Coil and Pole-group Connections


The synchronous alternator is the basic a.c. generator. It is called synchronous because its generated frequency is directly related to its number of armature and field poles and to its rotative speed. An individual coil of winding generates a full cycle of a.c. voltage each time it is swept by a pair of magnetic poles. The generated frequency is converted from cycles per pole pair to a machine basis by the following relation.


f = frequency in hertz

P = number of poles

S = speed in rpm

This relationship is of fundamental importance and can be easily followed if constructed from its basics.

  1. One full cycle of alternating current is developed for each pair of magnetic poles swept by a winding:
  2. There are a fixed number of poles in a full circle of construction or one revolution:

    Note: There must be an even-integer number of poles, as in a d.c. machine.

  3. The rotative speed is measured in revolutions per minute:
  4. There is 1 minute for each 60 seconds:

Gathering and cancelling, we have

Note: cycle/sec = Hertz

If the rotative speed is given in radians per second or ω, then

There are only a few recognized and used a.c. power frequencies. These are 25, 50, 60 and 400 Hz, with 50 Hz and 60 Hz by far the most common. 400 Hz is used almost exclusively for aircraft a.c. power because it allows small high speed machines which also require less magnetic structure size and weight. Any prime mover inherent rotative speed can be matched by a combination of pole and frequency combination.


Example 38.1

A large hydroelectric power plant is under consideration. Its hydraulic head or water level difference above and below the dam and its power requirement dictate its water turbine or runner must turn at from 137.00 rpm (14.387 rad/sec) to 140.00 rpm (14.661 rad/sec) to reach peak efficiency. Power required is 60 Hz.

  1. How many poles must a direct-connected alternator have?
  2. What rotational speed must be used?




Poles can only exist in even integer numbers. So we must have P = 52 poles

2. Using 52 poles, we have

Checking with rpm


rpm = 138.46 × 0.10472 = 14.500 rad/sec.

In a synchronous machine, the stator winding is the armature winding in which the operating e.m.f. is induced. Two types of windings namely: single-layer winding and double layer winding are considered.

38.5.1.  Single-layer Winding

The main difficulty with single-layer windings is to arrange the end connections so that they do not obstruct one another. Figure 38.9 illustrates one of the most common methods of arranging these end connections for a four-pole, three-phase synchronous machine having two slots per pole per phase, i.e., six slots per pole or a total of 24 slots.

Figure 38.9 End Connections of a Three-phase Single-layer Winding

In Figure 38.9 all the end connections are shown bent outward for clearness. In actual practice, the end connections are usually shaped in the manner shown in Figure 38.10 and in section in Figure 38.11. This method has the advantage that it requires only two shapes of end connections, namely, those marked (in Figure 38.11 which are brought straight out of the slots and bent so as to lie on a cylindrical plane, and those marked D. The later, after being brought out of the slots, are bent roughly at right angles, before being bent again to form an arch alongside the core.

Figure 38.10 End Connections of a Three-phase Single-layer Winding

Figure 38.11 Sectional View of End Connections

The connections of the various coils are more easily indicated by means of the developed diagram of Figure 38.12.

Figure 38.12 Three-phase Single Layer Winding

The solid lines represent the Red phase, the dot/dash lines the Yellow phase and the dashed lines the Blue phase. The width of the pole face has been made two-thirds of the pole pitch, a pole pitch being the distance between the centers of adjacent poles. The poles in Figure 38.12 are assumed to be behind the winding and moving towards the right from the right hand rule, bearing in mind that the thumb represents the direction of motion of the conductor relative to the flux, namely, to the left in Figure 38.12, the e.m.f.s in the conductors opposite the poles are as indicated by the arrow heads. The connections between the groups of coils forming any one phase must be such that all the e.m.f.s are assisting one another.

Since the stator has six slots per pole (in this case) and also since the rotation of the poles through one pole pitch corresponds to half a cycle of the e.m.f. wave or 180 electrical degrees, it follows that the spacing between two adjacent slots corresponds to 180/6, or 30 electrical degrees. Hence, if the wire forming the beginning of the coil occupying the first slot is taken to the red terminal R, the connection to the yellow terminal Y must be a conductor from a slot four slot-pitches ahead, namely, from the fifth slot, since this allows the e.m.f. in phase Y to lag the e.m.f. in phase R by 120°. Similarly, the connection to the blue terminal B must be taken from the ninth slot in order that the e.m.f. in phase B may lag the e.m.f. in phase Y by 120°. Ends R1, Y1 and B1 of the three phases can be joined to form the neutral point of a star-connected system. If the windings are to be delta connected, end R1 of phase R is joined to the beginning of Y, end Y1, to the beginning of B1 and the end B1 to the beginning of R, as shown in Figure 38.13.

Figure 38.13 Delta Connection of Windings

38.5.2.  Double-layer Winding

Consider a four-pole three-phase machine with two slots per pole per phase and two conductors per slot. Figure 38.14 shows the simplest arrangement of the end connections of one phase, the thick lines representing the conductors (and their end connections) forming, say, the outer lines, and the thin lines representing the conductors forming the inner layer of the winding. The coils are assumed full-pitch, i.e., the spacing between the two sides of each turn is exactly a pole pitch. The main feature of the end connections of a double-layer winding is the strap X1 which enables the coils of any one phase to be connected in such a way that all the e.m.f.s of that phase are assisting one another.

Since there are six slots per pole, the phase difference between the e.m.f.s of adjacent slots is 180/6, namely, 30 electrical degrees. Since there is a phase difference of 120° between the e.m.f.s of phases R and Y, there must be four slot pitches between the first conductor of phase R and that of phase Y. Similarly, there must be four slot pitches between the first conductors of phase Y and B. Hence, if the outer conductor of the third slot is connected to terminal R, the corresponding conductor in the seventh slot, in the direction of rotation of the poles, is connected to terminal Y and that in the eleventh slot to terminal B.

Figure 38.14 One Phase of a Three-phase Double-layer Winding

In general, the single-layer winding is employed where the machine has a large number of conductors per slot, whereas the double-layer winding is more convenient when the number of conductors per slot does not exceed eight.

38.5.3  Winding Pitch

A fractional-pitch double-layer winding coil does not have the same voltage being generated at the same time in each side of the coil. The coil winding distribution and the flux intensity distribution are both arranged in such a way that a sine-wave voltage results from a pole-phase group of windings. The individual coil side voltages must then be combined as phasors. The pitch factor is the ratio of the voltage generated by a fractional-pitch coil to the voltage generated by a full-pitch coil and is always less than 1. This is trigonometrically the sine of one half the coil span angle in electrical degrees.


kp = sin (p/2)        (38.6)

where, kp = pitch factor (dimension less) but ≤ 1

         p = coil span in electrical degrees when full pitch is 180 electrical degrees.

Since coil spans can only be constructed by integer number of lamination slots, and only a relatively few slots and resulting slot pitches are practical kp may be tabulated (see Table 38.1). Coil spans below two-thirds of the available slots are not normally used since they are of no advantage.

Table 38.1 contains all the likely pitch factors for a.c. motors and generators that have an integer number of slots per pole per phase.


Example 38.1

Find the pitch factor to be used in calculations involving a six-pole, three-phase alternating current generator. It has a total of 54 winding slots in the stator, and the coils span seven slots.


The 54 total slots divided by six poles gives 9 slots per pole. Nine slots per pole divided by three phase’s yields 3 slots per pole per phase. With nine slots per pole and a coil span of 7 slots, the factional pitch is 7/9. In electrical degrees, this is 180 (7/9) = 140 = p.


kp = sin 70° = 0.93969

If a full pitch coil voltage is unity then this generator has a pitch factor of kp = 0.93969. This can be checked from Table 38.1. If a coil enters one slot and leaves the core at the eighth slot away, connecting the entering slot, then it has a coil span of seven slots.


When several coils in a pole group are connected in series, their individual coil voltages are not directly additive unless two or more coils lie in the same slot. The distribution factor is related to but not identical to the pitch factor. The distribution factor is determined by the phase angle differences due to the individual coil placement, so its formulation is also based on phasor summation. The distribution factor is really related to the number of slots per pole per phase (n) and the number of electrical degrees between these slots (α).


Table 38.1 Pitch Factor kp for All Possible Slot Combinations for Three-Phase Alternators having 3 to 15 Slots Per Pole

In Figure 38.15, four slots per pole per phase are involved. The segments labelled coil voltage (Ec) are proportional to individual coil voltages whether or not they are chorded or one of fractional pitch. The long phasor (Epg) is the desired voltage for a phase group of coils. The relationship desired is then

Figure 38.15 Coil Distribution Factor

which reduces to

where Egpp refers to the voltage generated per pole per phase. This voltage can then be directly expanded by however many pole-phase groups are connected in series to get the full voltage per phase. This is because each pole-phase group is in time phase with other poles of the same phase. A typical four-pole machine would have all the four poles connected in series for its highest designed voltage. The other choice is usually two in parallel and two parallel groups in series for one half the e.m.f. of higher voltage connection.

The final generated voltage per phase must be corrected for the type of three-phase connection. If delta connected (Δ) the phase voltage is the line-to-line voltage. If it is wye-connected (Y or star), the phase voltage must be multiplied by to find the line-to-line voltage. Many industrial and commercial locations will take advantage of the relation and use the individual phase voltages or line to neutral as 120 V, and use the resulting wye-connected line-to-line voltage 208 V as a low to medium power three-phase combination. This 208/120 V common combination takes advantage of the factor.


Example 38.3

A small three-phase synchronous alternator can be connected in series wye for nominal 440 V line-to-line loads or parallel wye for nominal 220 V line to line loads. It has a total of 36 slots and is connected as a four-pole machine. Each of the 36 coils has 15 turns and is formed to span 8 slots (from 1 to 9). The field coils are adjusted to produce a flux of 0.006 Wb/pole. What is the line to line voltage at open circuit when connected parallel wye and turning at 1800 rpm (188.50 rad/sec)?


With 36 slots and 4 poles there are 9 slots/pole and 3 slots/pole/phase. Also ∝ = 180/9 = 20 electrical degrees/slot and with a span of 8 slots there are 160 electrical degrees/coil. From Table 38.1, kp = 0.98481 and from Table 38.2 kd = 0.95980. The turns per coil, N = 15 is also given. A pole-phase group is made of three coils, n = 3, so Nn = 15 × 3. For parallel, Wye connections each phase will have two permanently connected pole phase groups in series and two of these series connected groups in parallel. The connections will resemble Figure 38.8. As a result, Eq (38.6) voltages will be multiplied by 2 to get the per phase voltage. This, in turn, will be multiplied by to get the final line to line voltage.

Egpp= 4.44 (0.006) 15 (3) 60 (0.98481) 0.95980
= 68.031V per pole group


Table 38.2 Distribution Factor kd for Three-Phase Alternators

Since n is slots per pole per phase, n can only be an integer unless uneven coil groups are chosen. Similarly, ∝ in a three phase situation can only be 180/3n or, in general, 180/slots per pole. Then as in the case of kp, kd can also be tabulated.


Example 38.4

An eight-pole three-phase alternator is wound on a 72-slot core. Find the distribution factor of the winding.


Since there are 9 slots per pole and each pole is 180 electrical degrees. 180/9. α = 20 electrical degrees between adjacent slots. Thus, ∝ = 20° and n = 3

kd can be checked in Table 38.2



  ω is the angular velocity in radians/second

  ϕ is the flux in webers

  N is the number of turns per coil

  s is the relative speed in revolutions per second

A per phase per pole coil group is normally a permanent group of windings. Therefore, N turns per coil is modified to become Nn, where n is the number of coils per phase per pole. The above relation now becomes


Eav/pp = 4ϕN n f

f can be substituted for rad/sec

For the full voltage developed in a per pole per phase group of coils


Egpp = 4.44 ϕ Nn f kpkd        (38.9)

The same line-to-line voltage will hold in either unit.


When an alternator is in operation, a number of conditions have to be satisfied.

  1. The alternator must be connected to a prime mover and driven at its synchronous speed so that the proper a.c. frequency may be delivered. This is usually an exact requirement rather than approximate.
  2. The alternator must be properly synchronized before it is paralleled with any other alternators on the bus line. Steps 1 and 2 are quite simplified if the alternator runs by itself, a relatively rare situation.
  3. The voltage that the alternator is to deliver must be properly set by the adjustment of the rotating field excitation current. The field excitation is direct current to produce a steady magnetic field flux.

When there is no load on the alternator, its generated voltage per phase Egp, and its terminal voltage per phase Vp remain the same. The terminal voltage is reduced by the IR drop through the winding resistance.

The terminal voltage is also affected by the armature winding inductive reactance. Reactance and resistance effects are combined as phasors. The terminal voltage is also affected by the armature reaction, which is the result of the stator ampere turns acting across the main field an in effect more complex than that of a d.c. armature. The armature reaction has a variable effect since—depending on the load power factor—it can act to demagnetize the field or to increase the field magnetization.

As a result, the voltage regulation of an alternator is both variable and large. The same alternator may display substantial voltage drop or significant voltage rise, depending upon its load power factor. Voltage is controlled by external regulating circuits that vary rotating field winding current so that a constant voltage is delivered to the load.


The voltage regulation percentage for an a.c. alternator is figured in the same manner as for a d.c. generator.

Egp = internal generated voltage per phase at no load

Vp = terminal voltage per phase at no load

While in service the field current in a synchronous alternator under constant adjustment under the load power factor happens to be the small leading power factor that results in zero percent regulation for the generalized circuit it would be about 0.88 to 0.90 leading PF. Regulation depends upon the armature circuit inductive reactance or on the various modifications of the field magnetization due to the particular armature reaction.


Example 38.5

A typical Y-connected three-phase alternator is adjusted to its rated line-to-line voltage of 230.0 V while under its rated load and 80 per cent lagging power factor. The same field excitation current results in a load line-to-line voltage of 328.6 volt. What is its regulation?


Voltage generated per phase,

Example 38.6

The three phase alternator in Example 38.5 has a rated load voltage of 100 per cent while carrying an 80 per cent lagging power factor load at 100 per cent current. If the no-load voltage is 142.8 per cent of its rated voltage, what is its regulation?


Note: The per-unit method is a convenient way of comparing machines that are rated under different conditions.


There are two causes of voltage drop from no-load to full-load in separately excited d.c. generators: (1) armature circuit voltage drop; and (2) armature reaction. There are three causes of voltage drop in the (separately excited) synchronous alternator: (1) armature circuit voltage drop; (2) armature reactance; and (3) armature reaction. While the first two factors always tend to reduce the generated voltage, the third factor (armature reaction) may tend to increase or decrease the generated voltage. The nature of load affects the voltage regulation of the a.c. synchronous alternator.

As was the case in d.c. generators, if there is no-load on the (separately excited) alternator, the terminal voltage and the generated voltage are the same. The magnitude of the three causes of voltage drop in the synchronous alternator is solely a function of the load current Ia.

38.10.1  Unity Power Factor Loads

At unity power factor, the phase current in the armature Ia is in phase with the terminal phase voltage Vp by definition. The voltage drop per phase across the effective resistance of the armature Ia Ra is also always in phase with the armature current Ia. The inductive voltage drop due to armature reactance, IaXa, is always leading with respect to the current through it, since the current lags the voltage by 90° in a circuit possessing inductive reactance only. At unit PF, the armature reaction voltage drop Ear leads the armature current Ia which produced it, and is, therefore, always in phase with the armature reactance voltage drop IaXa. The basic generator equation may now be written for the unity power factor loads in complex form as the phasor sum

From the diagram of Figure 38.16(a) and Eq. 38.11, it may be seen that the terminal voltage Vp is always less than the generated voltage per phase by a total impedance drop Ia (Ra + j Xa), where jXa is the quadrature synchronous reactance voltage drop, or the combined voltage drop due to armature reactance and armature reaction.

38.10.2  Lagging Power Factor Loads

If the armature phase current lags the terminal voltage Vp by source angle θ as a result of an external load (primarily inductive) across the synchronous alternator, the voltages may be represented by the diagram shown in Figure 38.16(b).

The Ia Ra drop is still in phase with the armature phase currents, and the quadrature reactance and armature reaction voltage drops lead the armature current by 90°. It is simpler to indicate the value of Egp in terms of its horizontal and vertical components.

Figure 38.16 Relation Between Generated (No-load) and Terminal (Full-load) Voltages of a Synchronous Alternator for Three Types of Load Conditions (a) Unity PF Loads (b) Lagging PF Loads (c) Leading PF Loads (d) Negative Regulation at Leading PF Loads

To obtain the same rated terminal voltage per phase (Vp), a higher induced voltage per phase (Egp) is required at lagging power factor than at unity power factor.


Example 38.7

A 1000 kVA, 4600 V, 3ϕ, V -connected alternator has an armature resistance of 2 Ω per phase and a synchronous armature reactance of 20 Ω per phase. Find the full-load generated voltage per phase at (1) unity power factor and (2) 0.75 power factor lagging.


Ia Ra drop per phase =125 Α × 2 Ω = 250 V

Ia Xs dropper phase = 125 A × 20 Ω = 2500 V

  1. At unity PF
    Eg = (Vp + IaRa) + j IaXs
    = (2660 + 250) + j 2500
    = 2910 + j 2500 = 3836 V/phase


  2. At 0.75 PF lagging


    Egp = (Vp cos θ + IaRa) + j (Vp sin θ + IaXs)
    = [(2660 × 0.75) + 250] + j[(2660 × 0.66) + 2500]
    = 2245 + j 4259 = 4814 V/phase


  1. At unity PF and a lagging PF, the generated voltage per phase is greater than the terminal voltage per phase at all times.
  2. The voltage regulation is always positive.
  3. The solution is performed on a per phase basis because the definition of power factor is in these terms.

38.10.3  Leading Power Factor Loads

If the armature phase current Ia leads the terminal phase voltage Vp by some angle θ as a result of external load (containing a capacitor component) across the a.c. synchronous alternator, the voltages may be represented as shown in Figure 38.16(c). The Ia Ra drop is always in phase with the phase current in the armature, and the quadrature synchronous reactance drop Ia Xs leads the armature current by 90°. By indicating Egp in terms of the horizontal and vertical components, we find

It can be seen that for the same rated terminal phase voltage, less generated voltage is required for a leading power factor than for a lagging power factor.


Example 38.8

Repeat Example 38.7 to determine the generated voltage per phase at full load for: (1) a load of 0.75 PF leading; and (2) a load of 0.40 PF leading.


From Example 38.7

Vp = 2660 V
IaRa/phase = 250V
IaXs/phase = 2500V
  1. At 0.75 PF leading
    Egp = (Vp cos θ + IaRa) + j(Vp sin θ + IaXs)
    = [(2660 × 0.75) + 250] + j[(2660 × 0.66) + 2500]
    = 2245 – j 742 = 2364 V/phase


  2. At 0.40 PF leading
    Eg = [(2660 × 0.4) + 250] + j[(2660 × 0.9165) – 2500]
    = 1314 – j 62 = 1315 V/phase


  1. At both leading PFs, the generated voltage per phase is less than the terminal voltage per phase.
  2. At the given PFs, the voltage regulation is negative.

38.10.4  Voltage Regulation at Various Power Factors

Examples 38.7 and 38.8 illustrate two aspects of the effect of leading or lagging loads on alternator generated voltage and in turn, voltage regulation, namely,

  1. The lower the leading power factor, the greater the voltage rise from no load (Egp) to full load (Vp).
  2. The lower the lagging power factor, the greater the voltage decrease from no load (Egp) to full load (Vp).

Figure 38.17 provides the data of the above two examples. It may be noted that: (a) raising the power factor of a lagging load to unity power factor is still insufficient to produce zero per cent voltage regulation; (b) the terminal voltage will still drop as a purely resistive load is applied to the alternator; (c) at leading loads, the armature reaction is magnetizing and tends to produce additional generated voltage as load is applied, producing a negative regulator; and (d) at lagging loads, the armature reaction is demagnetizing and its effect in reducing the generated voltage, coupled with the internal armature resistive and reactive voltage drops, results in a rapid decrease in terminal voltage as load is applied.

Figure 38.17 Voltage Regulation of an Alternator at Various Power Factors with Field Current Adjusted to Provide Rated Voltage at Rated Load


Example 38.9

Calculate the voltage regulation at the four PFs computed in Examples 38.7 and 38.8, and as shown, respectively, in Figure 38.17.


  1. At 0.75 PF lagging
  2. At unity PF
  3. At 0.75 PF leading
  4. At 0.40 PF leading

38.10.5  A.C. Generators: A Comparison

The regulation of a separately excited d.c. generator (whose voltage drops with the application of load because of armature resistance and armature reactance) is inherently better than that of a separately excited a.c. synchronous alternator. Since commercial electrical loads are generally loads of a lagging nature, the voltage of a separately excited a.c. alternator will drop because of armature resistance, armature reactance and armature reaction. The effect of armature reaction in a d.c. generator is, primarily, cross magnetizing and slightly demagnetizing, whereas in an alternator, its demagnetizing component is the armature flux, ϕa sin θ.

The effects of armature reaction are usually compensated in a d.c. dynamo. The alternator’s inherently poor regulation is ignored and its output maintained at a constant terminal voltage by means of external voltage regulators. These automatically increase or decrease the field excitation from a d.c. generator (exciter) with changes in electric load and power factor. The exciter is usually on the same shaft as the prime mover and the alternator. Its characteristics are usually closely related to the alternator regulators.

38.10.6  Load Power Factor

Equations 38.12 and 38.13 can be stated in a combined fashion that holds for any power factor

or alternatively, in complex form,

For unity power factor cos θ is one, and sin θ is zero and Vp sin θ drops out. By comparing this with Eq. 38.12, it can be seen that Eq. 38.14 is a special case of Eq. 38.12 with cos θ = 1 and sin θ = 0.

with plus sign for unity or lagging power factor and minus sign for leading power factor.

38.10.7  Winding Resistance

The effective a.c. resistance of a particular winding is usually determined by using direct current and the voltmeter-ammeter method. A d.c. current is passed from terminal to terminal of either two of the three leads of a three phase winding or a complete single-phase winding. If the voltage drop from terminal to terminal is recorded at the same time as the current used, the d.c. resistance is R = E/Ia, Multiple readings are averaged for accuracy. This resistance is usually that of two phases, since the neutral point of a wye winding is usually not accessible. A test circuit is shown in Figure 38.18. In the less common delta wound alternator, the windings are usually permanently spliced together at the delta points. The resulting per phase resistance is




Since there are harmonics generated in the individual coils of the alternator windings, some high frequencies are also present even though their combined effect in a phase is minimal. High-frequency currents travel next the surface of a conductor (skin effect). The effective a.c. resistance is greater than the d.c. resistance. The factor of difference varies according to the base frequency at the alternator as well as the winding configuration, and is from 1.2 to 1.8. Resistance of the winding to the passage of alternating current is usually taken as 1.5 times the d.c. resistance for 60 Hz machines.


Ra = 1.5 Rd.c.        (38.19)

Figure 38.18 Winding Resistance and Synchronous Impedance Test Circuits (a) Per Phase Resistance Test (b) Open Circuit Test (c) Short Circuit Test

Ra is usually a very low resistance, particularly on large machines where it is an extremely small part of an ohm. Accurate determination of Ra is important in efficiency calculations. Voltmeter ammeter methods are usually used.

38.10.8  Synchronous Impedance

The phasor relation in Figure 38.19 holds for any power factor situation. All the sides of the diagram illustrated in Figure 38.19 contain the armature current as a multiplier. If Ia is divided into each side, a similarly shaped impedance triangle results, with Ra and Xa as the orthogonal sides and Xs as the hypotenuse. These values are, respectively, as follows.

  1. Ra is the effective a.c. resistance of the winding in whatever series and parallel coil combination is used.
  2. Xs is the effective combined winding reactance and reactance effect of the armature reaction. These effects operate together and Xs is the synchronous reactance, a per phase value.
  3. Zs is the phasor sum of Ra and Xs, and is defined as the synchronous impedance of the armature winding on a per phase basis.

The determination of the values of the Zs and Xs components of this impedance triangle is known as the synchronous impedance method. This procedure is widely used as well as universally recognized.

38.10.9  The Open-circuit Test and The Short-circuit Test

Two specific tests are necessary to determine the Zs or effective winding impedance. These are the open-circuit test and the short-circuit test. From these two tests and Ohm’s law for a.c. circuits, the impedance is determined where,

Figure 38.19 Alternator Impedance Relations, Impedance Triangle

The open-circuit voltage test is comparable to the d.c. machine open-circuit saturation curve. The alternator is driven at its synchronous speed. Field current is varied from a low value up to that sufficient for a voltage reasonably beyond the rated voltage. Data are recorded in suitable steps. If the alternator is a three-phase wye unit—as is usually the case—the line-to-line voltage E1 is divided by to find the per phase voltage. This step is not applicable to a single-phase unit. However, since the resistance Ra, the reactance Xs, and the impedance Zs are all per phase units, the data used to determine these values must be per phase also. The test circuit for open-circuit test is given in Figure 38.18(b).

For the short circuit test as shown in Figure 38.18(c), the machine is shut down and reconnected as shown. Ammeter protection switches are not shown, since the test will controllably build up and then reduce current. The ammeters for large machines require heavy shunts or suitable current transformers, since these currents may be in thousands of amperes in a larger unit.

It is not a simple thing to connect and drive a large alternator. Many large hydro electric units are not rotated at all until they are built into their location because of the magnitude and expense of a suitable prime-mover drive. On a large alternator, the only suitable load is the combined industrial, business, and domestic electrical customers of an entire city. The difficulty of performing a full-scale test with a controllable load is the real reason for the synchronous impedance test. Much less power is consumed in the prime mover since only the internal losses of the machine must be overcome. No external power is delivered either during the open-circuit or the closed-circuit test. As a result, only a small percentage of the full-load torque is needed.

The alternator is brought to its synchronous speed while short-circuited through the ammeters, as can be seen in Figure 38.18(c). Initially, the field current If is very low, zero, so that no abnormal short circuit currents are generated. Then, as the field current is increased, the short circuit currents are watched and recorded as Isc and its simultaneously corresponding If. A current at substantially beyond the normal rated current may be briefly reached with safety as long as the lines are not switched open. The data will show a straight line because the load is almost entirely inductive. As a result of the demagnetizing effect of the armature reaction, the machine is operating in the linear region of its saturation curve during this test. It is actually a situation where only the normal load currents and reasonable overload currents are carefully and controllably applied.

Since the currents and magnetic paths per phase are not identical, the Isc value used is the average of the three ammeter readings:

Example 38.10

A 1000 kVA, 2300 V, three phase, wye-connected synchronous alternator is tested to determine its synchronous impedance. The d.c. resistance between the two lines averages 0.412 Ω. The open-circuit voltage and the short-circuit current are determined to have the relation shown in Figure 38.20. Find the values of Ra, Zs and Xs assuming that Ra effective resistance is 1.5 lines the d.c. resistance.


Ra = 1.5 × 0.206 = 0.309 Ω


From Figure 38.20, at the open circuit per phase voltage corresponding to the rated line to line voltage, find the corresponding field current.

The corresponding field current If = 73 A

At the same If, Is 400 A

Figure 38.20 For Example 38.10

Note: Xs has very nearly the value Zs because of the comparatively small value of Ra.


Example 38.11

With the same alternator described in Example 38.10, calculate the percent regulation for full-load lagging power factor of 0.8.


IaRa = 251.0 × 0.309 = 77.6 V
IaXs = 251.0 × 3.31 = 831 V
cos θ = 0.8 so that
θ = 36.870″ and sin θ = 0.6

Little difference exists between the equivalent circuits of a single-phase a.c. synchronous alternator, as represented in Figure 38.21(a) and that of a three-phase a.c. synchronous alternator, as seen in Figure 38.21(b). Each phase winding of a three-phase alternator is assumed to have an effective armature resistance per phase of Ra, an effective armature reactance per phase of Xa, and a generated per phase voltage of Egp. Furthermore, if the load is balanced, it may be assumed that the voltage drop due to the effect of armature reaction is the same in each phase.

Figure 38.21 Equivalent Circuit of a Synchronous Alternator (a) Single Phase (b) 3-Phase, Wye Connected Equivalent Circuit of a Synchronous Alternator


The old proverb of ‘not putting all one’s eggs in one basket’ is the fundamental principle governing parallel operation. A utility system usually consists of several generating stations, as shown in Figure 38.22, with all operating in parallel. At each of the stations, there may be several a.c. alternators and/or d.c. generators, operating in parallel. There are numerous advantages to the subdivision of a generating station into smaller stations, from an economic as well as strategic point of view. These advantages also apply to the use of several smaller generating units rather than a single larger dynamo, although the latter is more efficient when loaded to its full capacity.

The reasons for parallelling generating sources have been discussed in Chapter 32. The same basic reasons for parallelling d.c. machinery hold for a.c. machinery also. Parallelling reasons may be summarized as follows.

  1. Local or regional power use may exceed the power of a single available generator.
  2. Parallel alternators allow one or more units to be shut down for scheduled or emergency maintenance, while the load is being supplied with power.
  3. Generators are inefficient at part load, so shutting down one or more generators allows the remaining load to be carried with less number of machines that are efficiently loaded.
  4. Loaded growth can be handled by added machines without disturbing the original installation.
  5. Available machine prime movers and generators can be matched for economic first cost and flexible use. The requirements for parallelling include those for d.c. machines in addition to a few others.
  6. The voltages must be the same at the parallelling point or junction even though it is not the same in the case of the alternators.
  7. The phase sequence for any multiple phase must be the same at the parallelling point.
  8. The incoming machine must be in phase at the moment of parallelling. It will continue to stay in phase under normal conditions after parallelling. It is important to recognize that phase sequence and in phase are not the same things.
  9. The line frequencies must be identical at the parallelling point. In the vast majority of cases, this means the same frequency at the generator because frequency changing is not economic. Mixed frequencies must be paralleled through some frequency conversion means for compatability at the point of interconnection.
  10. The prime movers must have relatively similar and drooping speed load characteristics. This is to prevent a machine with a rising speed-load characteristics from taking more and more of the load until it fails as a result of overload.

Violation of these requirements for parallelling would result in circulating currents between the machines varying from uneconomic, to serious, to disastrous.

38.12.1  Parallel Voltage Requirements

When one electrical device is in parallel with another, their voltages are identical at the parallelling point. If the devices are d.c. generators and set to different generating voltages Eg, a circulating current will exist between them. These currents will cause voltage drops through the armature resistances sufficient for the parallel point voltages to be identical, as they must be. This amounts to an I2R power loss. These losses heat the machines and in the case of a higher voltage machine additionally load the prime mover. Obviously, a mismatch is to be avoided.

In the synchronous alternator parallelling situation, it is the line-to-line voltage at the parallelling point that is forced to be the same, Ve1 = Ve2. As a result, in three phase the Vp of one generator must be matched to the other Vp. The machines may be of different rated voltages and connected through transformers. In fact, over a widespread regional grid, the interconnection path may be through quite a few transformers. As a result of intervening transformer action, the alternators may not have the same Vp voltages, but the effective transformed voltage will be the same; thus, the machines to be paralleled will have identical Vp voltages after parallelling.

The entering machine Vp, which at the moment is also its Egp, must match the bus voltage perhaps. Then the entering machine will need to be readjusted so that its total phasor situation will match the bus.

Figure 38.22 Single Line Diagram of a Typical a.c. Power System Showing Generation, Transmission, Distribution and Utilization of Electrical Energy

38.12.2  Phase Sequence Considerations

Phase sequence implies phase time sequence. Each alternator—as it is presented to a parallelling switch—must have the same phase sequence as the line at that point. If the bus has the sequence, say, A-B-C, and the incoming alternator has some other possible sequence, say, A-C-B a disastrous short-circuit condition exists. The resulting short-circuit current is alternately limited by the combined synchronous impedances of the windings involved. At the moment of switch closure, the current is still more because the armature reaction cross magnetization takes time to be fully established. Obviously, the out-of-phase sequence situation is to be most carefully avoided. This is easy to avoid with proper precautions.

Generator action involves motor action when current flows. The torque of any motor action is proportional to the armature circuit currents. Thus, an extremely high short circuit current involves extremely high transient torque. In the larger sizes, an out of phase parallelling attempt is nearly explosive and disastrous. Fortunately, a wrong sequence is easily corrected, once detected, by interchanging any two of the three phase leads.

In phase and in-phase sequence are different situations. Once a circuit is wired and tested, its phase sequence will not change unless some repair or component change causes an inadvertent interchange between two of the three phases. On the other hand, whether or not two alternators are in phase or out of phase must be determined each time alternators are paralleled.

If two identical-frequency, sine wave varying voltages are in phase it means that each voltage is at the same absolute value at any instant of time. This is shown in Figure 38.23(a). One of the many out-of-phase conditions is shown in Figure 38.23(b), where the two otherwise identical sine waves are 45 electrical degrees out of phase. If synchronous alternators are paralleled under these initial conditions, there are substantial circulating currents between machines with accompanying large torques.

Figure 38.23 In-phase Conditions (a) In Phase (B) 45 degrees Out of Phase

If the out-of-phase condition is small, the machines will usually pull into synchronism. When this takes place, there are mostly a few cycles of hunting while the condition damps out. Under normal conditions, with care and proper instrumentation, the transient is scarcely noticeable. The transient may cause an audible mechanical shock to the machines involved and the ammeters may flicker briefly. The difference between out of phase and out-of-phase sequence is very pronounced.

Synchronizing and parallelling of machines that are out of phase sequence cannot be achieved.

The trouble does not subside. The least that can be expected is that breakers will violently open the circuit. To conclude, these synchronous alternators must be in phase or nearly in phase to accomplish parallelling.

38.12.3  Identical Frequency Requirement

When in parallel, the various machines must have identical frequencies. The ideal design in this case is 60 Hz, and it is held very closely. The entire grid may drift to 60.01 or 59.99 Hz or more, very briefly, but it very, very closely achieves the following ideal:

As a result, 60 Hz synchronous motor driven clocks and timing devices do not require resetting for days at a time. The only exception is loss of time during a power failure.

The frequency of a large system is held closely to its ideal. The machine-to-machine frequency differences are held absolutely to zero. An individual machine or a group of machines may move slightly back or ahead in phase as an individual area load changes. It is by a small phase change that an individual machine may change its load current. However, when in parallel, a synchronous alternator does not pull far enough out of phase to slip or cycle and thus have generated a different frequency. The torque required to do so would normally exceed that available in the prime mover that drives the machine.

The period just before a parallelling switch is closed, the incoming alternator should be very closely at the same frequency as the bus. The acceptable difference between small 60 Hz machine frequencies is of the order of a small part of a cycle per second. On large public utility machines the difference is even smaller as some difference in frequencies may reasonably exist before parallelling.

In the period of time immediately after parallelling, the inertia of the incoming machine tends of keep the slightly different speed that it had when entering the parallel. However, the machine generated frequency has a fixed relation to its numbers of poles and its speed. As a result, the slightly different frequency of the incoming machine tends to cause a progressive phase difference, resulting in a retarding torque for the faster machine or an accelerating torque for the slower speed. If, as is usual the synchronized machines already on the bus have substantially more inertia, the incoming machine will be slowed to or accelerated to absolute synchronous speed. This process takes place in a relatively few cycles.

To conclude, the frequency of an alternator must be very closely matched to the bus to which it is to be paralleled.

38.12.4  Prime-Mover Torque Speed Relation

On a major public utility system, prime-mover speeds are kept so nearly constant that they can be safely identified as having that particular speed characteristic.

Each machine in a parallel combination must be driven with a suitable prime-mover characteristics. In the usual sense, a governed gasoline engine, diesel engine, reciprocating steam turbine, steam turbine, or gas turbine will all have drooping speed-load characteristics, meaning that as the torque load increases the speed droops or decreases. Each basic type of prime mover has given characteristics, some have 3 per cent, some 10 per cent and so on. Any parallelling combination should have a similar percentage speed droop to match a similar per cent load. This allows the alternators to share the load equitably.

If one prime mover has a substantially different speed-load relation than the other successful parallelling can only be accomplished in a narrow range of load. Since the alternators must run in synchronism, the one with soft speed characteristic (greater droop) will not carry its share of the load. With a number of parallel machines, an increase of load may actually overload one unit while only slightly increasing the load on the others.

A machine combination having a rising speed, load characteristic will soon assume all the load and continue to drive still more forcefully. As a result, the affected alternator is driven ahead in space and motorizes the others. While this lasts, the alternator with the rising-speed characteristic will carry all the outside load plus motorizing the other alternators. Their prime movers will rise in speed as they are unloaded, so synchronization is maintained. However, the affected rising speed characteristic will be so severely overloaded that it would be better not to have attempted paralleling.

The alternators that are to be paralleled must have similar prime mover speed characteristics. This speed characteristic must be drooping, since a rising speed characteristic is destructive.


Having understood the requirements for parallelling synchronous alternators, let us see how these required conditions are detected and applied.

38.13.1  Voltage Matching

The matching of voltage is easily determined in a straight forward manner. This is done with either one voltmeter switched from one to the other or with matched voltmeters.

38.13.2  Phase Sequence Matching

Phase sequence is determined by various simple procedures. It is not absolute phase sequence that is desired; rather, it is desired to know that the phase sequence of the bus and the entering alternator is the same. There are two very simple and very reliable circuits that show if the phase sequence is correct. There are the dark lamp circuit and the bright lamp circuit.

Figure 38.24(a) shows a typical dark lamp circuit with the synchronizing switch open, and the incoming alternator not yet turning, there is no opposing voltage for the lights. They will glow dimly and, steadily since they each see of the line-to-line voltage across two phases of the operating generator Figure 38.24(b) shows the bright lamp circuit. As the incoming alternator is brought up to speed, it has voltage and speed of its own. The lamps then see the difference of the voltage between alternators. The desired phase sequence condition is shown by whether the lamps go bright and dark together. If they twinkle on and off separately, there is a phase sequence error that must be corrected. The remedy is for any two of the three phase leads between the alternator and switch to be interchanged. The interchange must be the phase power leads. If the lamp leads are interchanged to produce a version of Figure 38.24(c), the lamps would come and go together and conceal a real wiring error. The bright lamp synchronizing system gives the same indication of phase sequence in that all lamps go bright, then dark, together with the correct phase sequence.

Figure 38.24 Lamp Methods of Synchronization (a) Dark Lamp Synchronizing Lamps (b) Bright Lamp Synchronizing Lamps (c) Two Bright One Dark Synchronizing Lamps

The two bright, one dark synchronizing lamp system shown in Figure 38.24(c) gives the opposite phase sequence indication. The lamps twinkle back and forth when the phase sequence is correct. Obviously, one must know which system is in use.

38.13.3  In-Phase Determination

The in-phase condition is shown (dark lamp) when all the lamps are dark. This condition is approached as the incoming machine speed approaches the bus frequency. Initially, the lamps will glow faintly. As the incoming machine is built up to voltage, but is not yet near the bus in frequency, the lamps glow quite brightly and steadily. As the frequencies are approaching matching condition, all the lamps go bright and dark together. The flashing frequency becomes longer and longer and longer and may become many seconds per second. Finally, the lamps go dark and stay dark for a few seconds. The middle of the dark period is the point of actual in-phase condition. When this point has been identified satisfactorily, the parallelling switch may be closed and the lamps will stay dark.

The last lamp synchronizing technique is known as two bright one dark synchronization, the rotating lamp synchronization, or the Siemen-Halske method. This circuit twinkles when the phase sequence is correct. Like both dark and bright lamp methods, it shows the approach of matching of the frequencies by longer and longer cycle change periods. The correct synchronizing point is shown by one dark light and the other two of the same brightness. Each lamp has the same range of bright and dark as in the other methods. However, no two lamps reach full brightness at the same out-of-phase angle. As the in-phase condition is approached, one light is out, one light slowly dims from full brightness and one light increases in brightness from a dim situation. When the two illuminated bulbs (or pairs) reach the same brightness, the switches are closed.


Note: If large voltages are present, no reasonable lamps can be used. In high-voltage units transformers are used to reduce lamp voltages. In medium installations, multiple series lamps are used as in Figure [38.24 (b) and (c)]. Only very low-voltage units would use the single lamp and resistor connection of Figure 38.24(a).

38.13.4  Frequency Synchronization

In all of the above methods, an interpretation of whether frequency synchronization is being approached can be made. With any of the systems, the lamps will appear continuously and dimly lit if the incoming frequency differs from the bus frequency by as much as 20 Hz. As the frequency of the incoming alternator is raised very nearly to that of the bus, the flashing rate becomes apparent. As synchronism is approached, the rate becomes a slow increase and decrease of brightness. At synchronous frequency, there is no change of light aspect. The individual circuit determines the lamp appearance that signifies the actual in-phase condition. If the incoming machine speed is increased and the lamp blink cycle gets longer, the first speed was below synchronous speed. If an increase in speed causes the lamp cycle to get shorter in time, the speed was already above synchronism and must be reduced.

38.13.5  Synchroscope Synchronization

In large central station installations, a device called a Synchroscope is used. A synchroscope has a rotating hand and a dial labelled with slow and fast direction arrows to show the incoming machine speed relation. In addition, an index point shows the actual in-phase position. During synchronization, as the incoming machine rotational speed approaches near synchronism, the speed of the synchroscope hand drops enough to become visible. The hand speed is proportional to the difference in speeds. The slow indication is accompanied with an arrow showing that counter clockwise hand rotation means below synchronous speed. Similarly, clockwise rotation means above synchronous speed. When the speeds are matched so that the hand speed is very slow, the hand is watched until it points to the index mark, whereupon the parallelling switch may be closed.

There are three types of synchroscopes: the polarized vane, the moving vane and the crossed coil. All are used similarly. They are used as a convenient and accurate means of routinely achieving synchronous speed and in-phase indications.

  1. The construction of a.c. machines is inside out in relation to d.c. machines.
  2. No commutator function is needed.
  3. Armature coils are larger than field coils.
  4. Most a.c. machines have armature in the stator position and field in the rotor.
  5. Since no polarity switching is required collector rings are usually used.
  6. The armature and field coils are both placed in slots in the punched magnetic structure.
  7. It is easier to cool the stator than the rotor which is an advantage of a.c. construction.
  8. The fixed and outside armature has a complete ring of teeth and slots on its inner surface.
  9. All the slots are filled with similar and symmetrical coils.
  10. With salient pole machine construction the number of poles in visible.
  11. The stator tooth structure becomes stronger as it grows deeper.
  12. A rotor tooth structure becomes weaker as it grows deeper.
  13. A thin lamination has less eddy current but is difficult to handle.
  14. A stock thickness of 0.35 mm has long been used for 60 Hz a.c. machines.
  15. In an a.c. generator, the rotating conductor is connected to the load through slip rings and brushes.
  16. Lap winding is much more common with a.c. machines owing to shorter coil connections.
  17. The majority of a.c. machine coils are of fractional pitch type.
  18. The majority of machines use double-layer winding arrangement.
  19. In a synchronous machine the stator winding is that winding in which the operating e.m.f. is induced.
  20. The single-layer winding is employed where the machine has a large number of conductors per slot.
  21. The double-layer winding is more convenient when the number of conductors per slot does not exceed eight.
  22. Egp = 4.44ϕNnkpkd V
  23. Percentage voltage regulation
  24. The nature of load affects the voltage regulation of the a.c. synchronous alternator.
  25. Each phase winding of a three-phase alternator is assumed to have an effective armature resistance per phase of Ra, an effective armature reactance per phase of Xa, and a generated per phase voltage of Egp.
  26. In the synchronous alternator parallelling situation: (1) The line-to-line voltage at the parallelling point must be the same. (2) The out-of-phase sequence is to be carefully avoided. (3) The frequency of an alternator must be very closely matched to the bus to which it is to be paralleled.
  27. Phase sequence matching is performed by taking resort to the lamp methods of synchronization or with the help of a synchroscope.
  1. In an alternator terminal voltage will rise
    1. When a unity power factor load is thrown off
    2. When a leading load is thrown off
    3. When a lagging load is thrown off
    4. None of the above
  2. To have two alternators in parallel, which of the following factors should be identical for both?
    1. Voltage
    2. Phase sequence
    3. Frequency
    4. All of the above
  3. At leading power factor operation, an alternator
    1. Is over excited
    2. Is under excited
    3. Has residual magnetism
    4. Has negative torque angle
  4. When an alternator feeds a resistive or inductive load, regulation is
    1. Always positive
    2. Always negative
    3. All of the above
    4. None of the above
  5. The standard practice of construction now a days is to have
    1. Rotating armature
    2. Rotating field
    3. Either of the above
    4. None of the above
  6. In an alternator, the armature reaction influences the magnitude of
    1. No load loss
    2. Speed of the machine
    3. Terminal voltage per phase
    4. Wave form of generated voltage
  7. What will happen if a stationary alternator is connected to a live bus bar?
    1. It will decrease bus bar voltage
    2. It is likely to run as a synchronous motor
    3. It will get short circuited
    4. It will disturb generated e.m.f. of other paralleled alternators
  8. The dark and bright lamp method is used in an alternator for
    1. Balancing of load
    2. Phase sequence
    3. Transfer of load
    4. Synchronizing
  9. Voltage generated per phase in an alternator is proportional to
    1. Flux per pole
    2. Frequency of waveform
    3. Number of turns in armature
    4. All of the above
  10. In a cylindrical rotor, how much portion of the rotor is waved?
    1. Half
    2. Full
    3. One-third
    4. Two-third
  11. Conventional rotating exciter is basically a
    1. d.c. shunt generator
    2. d.c. series generator
    3. d.c. series motor
    4. d.c. shunt motor
  12. With reduction of load on an alternator
    1. The frequency increases
    2. The frequency decreases
    3. The frequency oscillates
    4. The frequency remains constant
  13. If the field of one of the alternators running in parallel is adjusted it will
    1. Reduce its speed
    2. Change its load
    3. Change its power factor
    4. Change its frequency
  14. Why hydrogen is used in a large alternator?
    1. To cool the machine
    2. To reduce eddy current losses
    3. To reduce distortion of waveform
    4. To strengthen the magnetic field
  15. When the voltage rating of an alternator is low, it is comparatively
    1. More efficient
    2. Operating of high rpm
    3. More costly
    4. Larger in size
  1. (c)
  2. (d)
  3. (b)
  4. (a)
  5. (b)
  6. (c)
  7. (c)
  8. (d)
  9. (d)
  10. (d)
  11. (a)
  12. (a)
  13. (c)
  14. (a)
  15. (d)
  1. What is meant by saying that most a.c. machines are inside out in relation to d.c. machines?
  2. Why is a commutator not necessary in usual a.c. motors and generators?
  3. What is meant by the terms rotor and stator as distinct from the terms armature and field?
  4. What is meant by chorded windings?
  5. There is hierarchy of windings, starting with an individual armature winding coil and ending with a completely connected armature circuit. What part of this succession is a pole-phase group?
  6. If each pole-phase group of coils is gathered into total phase groups, all poles of a particular phase are interconnected. In what manner can this phase interconnection be performed so that two different voltage levels can be accommodated?
  7. In addition to voltage-level consideration, what other major precautions must be taken in connecting a phase group of coils that connect various poles?
  8. Why is a normal d.c. generator called a synchronous alternator?
  9. How many electrical degrees are passed in one revolution of a six-pole synchronous alternator?
  10. How many cycles of alternating current are generated in one revolution of a 14-pole synchronous alternator?
  11. If a four-pole, three-phase winding is placed in a stator that has 48-slots.
    1. How many slots are there per phase?
    2. How many slots per pole per phase?
  12. What frequency is generated by a six-pole alternator that rotates at 1200 rpm?
  13. What frequency is generated by a 10-pole alternator that rotates at 62.83 rad/sec?
  14. A large diesel engine is to be used as a prime mover in a standby or emergency power plant. Its normal rated speed is 440 rpm and it can be adjusted to operate a small range above or below this point.
    1. How many poles should be specified in a directly coupled alternator?
    2. What operating speed should be used to produce 60 Hz?
  15. What is the difference between a salient pole and a distributed pole field structure?
  16. Why is rms voltage wanted rather than average voltage?
  17. Describe the meaning of pitch factor kp.
  18. Why is kp never larger than unity?
  19. Describe the meaning distribution factor kd?
  20. Why is distribution factor always less than unity if there is more than one coil and the coils do not lie in the same slots?
  21. Why is the per pole per phase group a convenient quantity?
  22. What is the effect of stator winding impedance on the voltage regulation of an alternator?
  23. What is the effect of armature reaction on the voltage regulation of an alternator?
  24. Why is the simple d.c. resistance of the armature phase windings modified by a factor of 1.5 to achieve effective d.c. resistance?
  25. Why is the short circuit test portion of the synchronous impedance test not damaging to the alternator?
  26. A wye-connected, three-phase a.c. generator is delivering power to a three-phase line. The line-to-line voltage is 460 V. The line currents are 7.73 A and the total voltage as 5.12 kW. What are the following:
    1. Phase voltage,
    2. Phase current, and
    3. Load power factor?
  27. What is (a) the Egp and (b) the voltage regulation of an alternator that has Ra = 0.152 Ω, and Xs = 9.33 Ω and delivers 230 V line-to-line at 9.5 A pealine? Use unity power factor.
  28. Why must voltages be the same at the parallelling junction point?
  29. Describe the meaning of phase sequence.
  30. How is being in phase different from being in phase sequence?
  31. Why do synchronous alternators stay in phase after parallelling?
  32. Why is it necessary that a prime mover have a drooping speed characteristic?
  33. Why cannot bright lamp synchronizing achieve exact three phase synchronizing?
  34. Why can two bright, one dark lamp synchronization achieve very close in phase synchronism when other lamp methods cannot?
  35. Why is it difficult to determine if a close but not exact synchronization is above or below speed with the various lamp methods?
  36. Why is one of the forms of synchroscopes used in large unit parallelling?

9.  1080 electrical degrees

10.  7 cycles

11.  (a) 16 slots per phase, (b) 4 slots per pole per phase

12.  60 Hz

13.  50 Hz

14.  (a) 16 poles; (b) 450 r.p.m.

26.  (a) 265.6V, (b) 7.738, (c) 83.1 per cent

27.  (a) 160.9V, (b) 21.13 per cent.