DC GENERATORS

DC GENERATORS

The dc machine operating as a generator is driven by a prime mover at a constant speed and the armature terminals are connected to a load. In many applications of dc generators, knowledge of the variation of the terminal voltage with load current, known as the external or (terminal) characteristic, is essential.

Introduction

Applications such as light bulbs and heaters require energy in electrical form. In other applications, such as fans and rolling mills, energy is required in mechanical form. One form of energy can be obtained from the other form with the help of converters. Converters that are used to continuously translate electrical input to mechanical output or vice versa, are called electric machines. The process of translation is known as electromechanical energy conversion. An electric machine is therefore a link between an electrical system and a mechanical system, as shown in Fig. 1.1. In these machines, the conversion is reversible. If the conversion is from mechanical to electrical, the machine is said to act as a generator. If the conversion is from electrical to mechanical, the machine is said to act as a motor. Hence, the same electric machine can be made to operate as a generator as well as a motor. Machines are called ac machines (generators or motors) if the electrical system is ac and dc machines (generators or motors) if the electrical system is dc

Fig: Electromechanical energy conversion

Note that the two systems in Fig. 1.1, electrical and mechanical, are different in nature. In the electrical system the primary quantities involved are voltage and current, while the analogous quantities in the mechanical system are torque and speed. The coupling medium between these different systems is the field, as illustrated in Fig. 1.2. 

Fig.1.2: Coupling field between electrical and mechanical systems

 

Electromagnetic conversion

Three types of electrical machines (dc, induction, and synchronous) are used extensively for electromechanical energy conversion. In these machines, conversion of energy from electrical to mechanical form or vice versa, results from the following two electromagnetic phenomena:

1.      When a conductor moves in a magnetic field, voltage is induced in the conductor.

2.      When a current-carrying conductor is placed in a magnetic field, the conductor experiences a mechanical force.

These two effects occur simultaneously whenever energy conversion takes place from electrical to mechanical or vice versa. In motoring action, the electrical system makes current flow through conductors that are placed in the magnetic field. A force is produced on each conductor. If the conductors are placed on a structure free to rotate, an electro-magnetic torque will be produced, tending to make the rotating structure rotate at some speed. If the conductors rotate in a magnetic field, a voltage will also be induced in each conductor. In generating action, the process is reversed. In this case, the rotating structure, the rotor, is driven by a prime mover such as a steam turbine or a diesel engine. A voltage will be induced in the conductors that are rotating with the rotor. If an electrical load is connected to the winding formed by these conductors, a current will flow, delivering electrical power to the load. Moreover, the current flowing through the conductor will interact with the magnetic field to produce a reaction torque, which will tend to oppose the torque applied by the prime mover. Note that in both motoring and generating actions, the coupling magnetic field is involved in producing a torque and an induced voltage.

Motional Voltage, e

An expression can be derived for the voltage e induced, in a conductor moving in a magnetic field. As shown in Fig. 1.3a, if a conductor of length l moves at a linear speed v in a magnetic field B, the induced voltage in the conductor is

e = Blv                                                            …(1.1)

B, v and l are mutually perpendicular. The polarity of the induced voltage can be determined from the so-called right-hand screw rule.

These three quantities v, B, and e are shown in Fig. 1.3b as three mutually perpendicular vectors. Turn the vector v toward the vector B. If a right-hand screw is turned in the same way, the motion of the screw will indicate the direction of positive polarity of the induced voltage. 

(a)                                            (b)

Fig 1.3: Motional Voltage. (a) Conductor moving in the magnetic field.

(b) Right-hand screw rule. 

The voltage induced in a conductor can also be obtained by Faraday’s law, which states that the voltage induced is equal to the rate of change of flux linkage.

Electromagnetic Force, f

For the current-carrying conductor shown in Fig. 1.4a, the force (known as Lorentz force) produced on the conductor is

f = B l i                                                            …(1.2)

where B, f, and i are mutually perpendicular. The direction of the force can be determined by using the right-hand screw rule, illustrated in Fig. 1.4b.

Turn the current vector i toward the flux vector B. If a screw is turned in the same way, the direction in which the screw will move represents the direction of the force f.

Note that in both cases (i.e., determining the polarity of the induced voltage and determining the direction of the force) the moving quantities (v and i) are turned toward B to obtain the screw movement.

Equations 1.1 and 1.2 can be used to determine the induced voltage and the electromagnetic force or torque in an electric machine. There are, of course, other methods by which these quantities (e and f) can be determined.

Fig 1.4: Electromagnetic force. (a) Current-carrying conductor moving in a magnetic field. (b) Force direction.

Basic Structure of Electric Machines

The structure of an electric machine has two major components, stator and rotor, separated by the air gap.

Stator:            This part of the machine does not move and normally is the outer frame of the machine.

Rotor:             This part of the machine is free to move and normally is the inner part of the machine.

Both stator and rotor are made of ferromagnetic materials. In most machines, slots are cut on the inner periphery of the stator and outer periphery of the rotor structure, as shown in Fig.1.5(a). Conductors are placed in these slots. The iron core is used to maximize the coupling between the coils (formed by conductors) placed on the stator and rotor, to increase the flux density in the machine and to decrease the size of the machine. If the stator or rotor (or both) is subjected to a time-varying magnetic flux, the iron core is laminated to reduce eddy current losses. The thin laminations of the iron core with provisions for slots are shown in Fig. 1.6 

Fig 1.5: Structure of electric machines. (a) Cylindrical machine (uniform-air gap).

 (b) Salient-pole machine (non-uniform-air gap).

Fig 1.6: Laminations. (a) Stator. (b) Rotor. 

The conductors placed in the slots of the stator or rotor, are interconnected to form windings. The winding in which voltage is induced is called the armature winding. The winding through which a current is passed to produce the primary source of flux in the machine is called the field winding. Permanent magnets are used in some machines to provide the major source of flux in the machine.

Rotating electrical machines take many forms and are known by many names. The three basic and common ones are dc machines, induction machines, and synchronous machines. There are other machines, such as permanent magnet machines, hysteresis machines, and stepper machines.

DC MACHINES

The dc machines are versatile and extensively used in industries. A wide variety of volt-ampere or torque-speed characteristics can be obtained from various connections of the field windings. Although a dc machine can operate as either a generator or a motor, at present its use as a generator is limited because of the widespread use of ac power. The dc machine is extensively used as a motor in industry. Its speed can be controlled over a wide range with relative ease. Large dc motors (in tens or hundreds of horsepower) are used in machine tools, printing presses, conveyors, fans, pumps, hoists, cranes, paper mills, textile mills, rolling mills, and so forth. DC motors still dominate as traction motors used in transit cars and locomotives. Small dc machines (in fractional horsepower rating) are used primarily as control devices – such as tachogenerators for speed sensing and servomotors for positioning and tracking. The dc machine definitely plays an important role in industry.

CONSTRUCTION

In a dc machine, the armature winding is placed on the rotor and the field windings are placed on the stator. These windings are shown in Fig 1.7. The essential features of a two-pole dc machine are shown in Fig. 1.8. The stator has salient poles that are excited by one or more field windings, called shunt field windings and series field windings. The field windings produce an air gap flux distribution that is symmetrical about the pole axis (also called the field axis, direct axis, or d-axis).

 

Fig. 1.7: DC Machine. (a) Stator (b) Rotor

(c) Schematic cross-sectional view for a two-pole machine. 

The voltage induced in the turns of the armature winding is alternating. A commutator-brush combination is used as a mechanical rectifier to make the armature terminal voltage unidirectional and also to make the mmf wave due to the armature current fixed in space. The brushes are so placed that when the sides of an armature turn (or coil) pass through the middle of the region between field poles, the current through it changes direction. As a consequence, the mmf due to the armature current is along the axis midway between the two adjacent poles, called the quadrature (or q) axis. In the schematic diagram of Fig. 1.8, the brushes are shown placed on the q-axis to indicate that when a turn (or coil) undergoes commutation its sides are in the q-axis. However, because of the end connection, the actual brush positions will be approximately 90^o from the position shown in Fig. 1.8.

Fig. 1.8: Schematic diagram of a dc machine.

Note that because of the commutator and brush assembly, the armature mmf (along the q-axis) is in quadrature with the field mmf (d-axis). This positioning of the mmf’s will maximize torque production. The armature mmf axis can be changed by changing the position of the brush assembly as shown in Fig.1.9. For improved performance, interpoles (in between two main field poles) and compensating windings (on the face of the main field poles) are required.

Fig. 1.9: Shift of brush position

EVOLUTION OF DC MACHINES

Consider a two-pole dc machine as shown in Fig. 1.10a. The air gap flux density distribution of the field poles is shown in Fig. 1.10b. Consider a turn a-b placed on diametrically opposite slots of the rotor. The two terminals a and b of the turn are connected to two slip rings. Two stationary brushes pressing against the slip rings provide access to the revolving turn a-b.

The voltage induced in the turn is due to the voltage induced in the two sides of the turn under the poles. Using the concept of “conductor cutting flux” (Eq. 1.1), these two voltages are in series and aid each other. The voltage induced in the turn, e_ab (same as the voltage e₁₂ across the brushes), is alternating in nature, and its waveform is the same as that of the flux distribution wave in space.

Fig. 1.10: Induced voltage in a dc machine. (a) Two-pole dc machine.

(b) Induced voltage in a turn. 

Let us now replace the two slip rings by two commutator segments (which are copper segments separated by insulation materials) as shown in Fig. 1.11a. Segment C_a is connected to terminal a of the turn and segment C_b to terminal b of the turn. For counterclockwise motion of the rotor, the terminal under the N pole is positive with respect to the terminal under the S pole. Therefore, brush terminal B₁ is always connected to the positive end of the turn (or coil) and brush terminal B₂ to the negative end of the turn (or coil). Consequently, although the voltage induced in the turn, e_ab, is alternating, the voltage at the brush terminals, e₁₂, is unidirectional as shown in Fig. 1.11b. This voltage contains a significant amount of ripple. In an actual machine, a large number of turns are placed in several slots around the periphery of the rotor. By connecting these in series through the commutator segments (to form an armature winding), a good dc voltage (having a small amount of ripple) can be obtained across the brushes of the rotor armature as shown in Fig.1.11c. 

Fig. 1.11: Voltage rectification by commutators and brushes. (a) Dc machine with commutator segments. (b) Single turn machine. (c) Multiturn machine.

Note that turn a-b is short-circuited by the brushes when its sides pass midway between the field poles (i.e., the q-axis). In the case of a dc motor, current will be fed into the armature through the brushes. The current in the turn will reverse when the turn passes the interpolar region and the commutator segments touch the other brushes. This phenomenon is illustrated by the three positions of the turn in Fig. 1.12.

Fig. 1.12: Current reversal in a turn by commutator and brushes. (a) End a touches brush B1; current flows from a to b. (b) The turn is shorted; turn is in interpolar region. (c) End a touches brush B2; current flows from b to a.

ARMATURE WINDINGS

As stated earlier, in the dc machine the field winding is placed on the stator to excite the field poles, and the armature winding is placed on the rotor so that the commutator and brush combination can rectify the voltage. There are various ways to construct an armature winding. Before these are discussed, some basic components of the armature winding and terms related to it are defined.

            A turn consists of two conductors connected to one end by an end connector.

            A coil is formed by connecting several turns in series.

            A winding is formed by connecting several coils in series.

The turn, coil, and winding are shown schematically in Fig. 1.13. The beginning of the turn, or coil, is identified by the symbol S and the end of the turn or coil by the symbol F. 

Fig. 1.13: Turn, coil, and windings.

Most dc machines, particularly larger ones, have more than two poles, so most of the armature conductors can be in the region of high air gap flux density. Figure 1.14 shows the stator of a dc machine with four poles. This calls for an armature winding that will also produce four poles on the rotor. The air gap flux density distribution due to the stator poles is shown in Fig. 1.14b. Note that for the four-pole machine, in going around the air gap once (i.e., one mechanical cycle) two cycles of variation of the flux density distribution are encountered. If we define

q_md = mechanical degrees or angular measure in space

q_ed = electrical degrees or angular measure in cycles

then, for a p-pole machine,

q_ed = (p/2) q_md                                      …(1.3)

The distance between the centers of two adjacent poles is known as pole pitch or pole span. Obviously,

One pole pitch = 180^o_ed = 360^o_md/p 

Fig. 1.14: Mechanical and Electrical degrees. (a) Four-pole dc machine.

(b) Flux density distribution.

The two sides of a coil are placed in two slots on the rotor surface. The distance between the two sides of a coil is called the coil pitch. If the coil pitch is one pole pitch, it is called a full-pitch coil. If the coil pitch is less than one pole pitch, the coil is known as a short-pitch (or fractional-pitch) coil. Short-pitch coils are desirable in ac machines for various reasons. The dc armature winding is mostly made of full-pitch coils.

There are a number of ways in which the coils of the armature windings of a dc machine can be interconnected. Two kinds of interconnection, lap and wave, are very common. These are illustrated in Figs. 1.15 and 1.16, respectively. 

Wave Winding

The layout of a wave-wound armature winding is shown in Fig. 1.16a. The coil arrangement and the end connections are illustrated by the dark lines shown in Fig. 1.16a for two coils. One end of the coil starts at commutator bar 2 and the coil sides are placed in slots 7 and 12. The other end of the coil is connected to commutator bar 13. The second coil starts at this commutator bar and is placed in slots 18 and 2 and ends on commutator bar 3. The coil connections are continued in this fashion. The winding is called a wave winding because the coils are laid down in a wave pattern.

Note that between two adjacent commutator bars there are p/2 coils connected in series, as opposed to a single coil in the lap winding. Between two adjacent brushes there are 1/p of the total commutator bars. Between two adjacent brushes, therefore, there are (p/2)(1/p) or ½ of all the coils. This indicates that in the wave winding the coils are arranged in two parallel paths, irrespective of the number of poles, as illustrated in Fig. 1.18b. Note also in Fig.1.18a that the two brushes of the same polarity are connected essentially to the same point in the winding, except that there is a coil between them. However, between the positive and negative brushes, a large number of coils are connected in series. Although two brush positions are required, one positive and one negative, in a wave winding (and this minimum number is often used in small machines), in large machines more brush positions are used in order to decrease the current density in the brushes.

In wave windings, the number of parallel paths (a) is always two and there may be two or more brush positions.

Also note from Figs.1.15a and 1.16a that when the coil ends pass the brushes, the current through the coil reverses. This process is known as commutation, and it happens when the coil sides are in the interpolar region. During the time when two adjacent commutator bars make contact with a brush, one coil is shorted by the brush in the lap winding and p/2 coils in the wave winding. The effects of these short-circuited coils, undergoing commutation, will be discussed later.

In small dc motors, the armature is machine wound by putting the wire into the slots one turn at a time. In larger motors, the armature winding is composed of prefabricated coils that are placed in the slots. Because many parallel paths can be provided with a lap winding, it is suitable for high-current, low voltage dc machines, whereas wave windings having only two parallel paths are suitable for high-voltage, low-current dc machines. 

Fig. 1.16: Wave winding. (a) Unrolled winding. (b) Equivalent coil representation. 

ARMATURE VOLTAGE

As the armature rotates in the magnetic field produced by the stator poles, voltage is induced in the armature winding. In this section an expression will be derived for this induced voltage. We can start by considering the induced voltage in the coils due to change of flux linkage (Faraday’s law) or by using the concept of “conductor cutting flux”. Both approaches will provide the same expression for the armature voltage.

The waveform of the voltage induced in a turn is shown in Fig. 1.10b, and because a turn is made of two conductors, the induced voltage in a turn a-b (Fig. 1.10) from Eq. 1.1 is

 e_t = 2B(q)lw_mr                                                 …(1.4)

 where l is the length of the conductor in the slot of the armature, w_m is the mechanical speed, r is the distance of the conductor from the center of the armature, that is, the radius of the armature.

The average value of the induced voltage in the turn is

            e_t = 2B(q)lw_mr                                                 …(1.5)

 Let

F = flux per pole

                 A = area per pole = (2prl/p)

 Then

                                                                                              B(q) = (F/A) = (fp/2prl)                                 …(1.6)

From Eqs. 1.5 and 1.6,

                    e_t = (Fp/p) w_m                                                 …(1.7)

 The voltages induced in all the turns connected in series for one parallel path across the positive and negative brushes will contribute to the average terminal voltage E_a. Let

N = total number of turns in the armature winding

                                              a = number of parallel paths

Then

E_a =   (N/a) e_t                                       …(1.8)

From Eqs. 1.7 and 1.8,

    E_a = (Np/pa) F w_m

          E_a = K_a F w_m                                      …(1.9)

 where K_a is known as the machine (or armature) constant and is given by

 K_a = (Np/pa)                                       …(1.10)

or

K_a = (Zp/2pa)                                      …(1.11)

where Z is the total number of conductors in the armature winding. In the MKS system, if F is in webers and w_m in radians per second, then E_a is in volts.

This expression for induced voltage in the armature winding is independent of whether the machine operates as a generator or a motor. In the case of generator operation it is known as generated voltage, and in motor operation it is known as back emf. 

Alternative Derivation

 

Consider a conductor rotating at n rpm in the magnetic field of p poles having a flux of f per pole. The total flux cut by the conductor in n revolutions (i.e. in one minute is pfn; hence the flux cut per second, giving the induced voltage e is

                                              e = rate of change of flux linkage = pfn/60   V                                                                    

If there is a total of Z conductors on the armature connected in  ‘a’  parallel paths, then the effective number of  conductors in series is  Z/a.  Hence the total emf induced,

As  w_m = 2pn/60, the above Eqn. becomes

Thus, for a particular machine

E_{a =} K_a f w_m    V 
where

K_a is known as the machine (or armature) constant.   

DEVELOPED (OR ELECTROMAGNETIC) TORQUE

There are various methods by which an expression can be derived for the torque developed in the armature (when the armature winding carries current in the magnetic field produced by the stator poles). However, a simple method is to use the concept of Lorentz force, as illustrated by Eq. 1.2.

Consider the turn a a^’b^’b shown in Fig. 1.17, whose two conductors aa^’ and bb^’ are placed under two adjacent poles. The force on a conductor (placed on the periphery of the armature) is

f_c = B(q)li_c = B(q)l (I_a/a)                                  …(1.12)

where i_c is the current in the conductor of the armature winding, I_a is the armature terminal current

The torque developed by a conductor is

T_c = f_c r                                                …(1.13)

The average torque developed by a conductor is

T_c = B (q) l (I_a/a) r                                           …(1.14)

From Eqs. 1.6 and 1.14

T_c = (FpI_a / 2pa)                                             …(1.15)

All the conductors in the armature winding develop torque in the same direction and thus contribute to the average torque developed by the armature. The total torque developed is

T = 2NT_c                                                         …(1.16)

From Eqs. 1.15 and 1.16

T = (N F p / p a) I_a = K_a F I_a                                     …(1.17)

In the case of motor action, the electrical power input (E_a I_a) to the magnetic field by the electrical system must be equal to the mechanical power (Tw_m) developed and withdrawn from the field by the mechanical system. The converse is true for generator action. This is confirmed from Eqs. 1.9 and 1.17. Electrical power,

E_a I_a = K_a F w_m I_a = T w_m,      mechanical power       …(1.17a)

Fig. 1.17: Torque production in a dc machine.