Comprehensive Study Notes on D.C. Generators: Generators Principles, Construction, and Operation

Introduction to D.C. Machines and Generators

While a significantly higher percentage of electrical machines in active service are alternating current (a.c.) machines, direct current (d.c.) machines maintain considerable industrial importance. The primary advantage of the d.c. machine, particularly the d.c. motor, lies in its ability to provide fine control over speed—an advantage not claimed by any a.c. motor. Historically, d.c. generators were common, but they are currently less prevalent because direct current is now primarily obtained from an a.c. supply using rectifiers. Nevertheless, understanding d.c. generators is a vital logical introduction to the behavior of d.c. motors, especially since many industrial d.c. motors operate as generators for brief periods during their operation cycle.

Fundamental Principles of Electric Generators

An electric generator is defined as a machine that converts mechanical energy into electrical energy. The operation is based on the fundamental principle that whenever magnetic flux is cut by a conductor, an e.m.f. is induced. If the conductor circuit is closed, this e.m.f. causes a current to flow. The direction of the induced e.m.f., and consequently the direction of the current, is determined by Fleming’s Right-Hand Rule. The three essential components required for a generator to function are a magnetic field, a conductor or group of conductors, and the motion of the conductor relative to the magnetic field.

Operation of the Simple Loop Generator

To understand the generation process, consider a single-turn loop labeled ABCD rotating clockwise at a constant speed within a uniform magnetic field. As the loop rotates, the flux linking the coil sides AB and CD changes continuously. The total induced e.m.f. is the sum of the e.m.f.s induced in both coil sides. The generation cycle involves several specific positions. In Position 1, the coil sides move parallel to the flux, resulting in zero generated e.m.f. In Position 2, the sides move at an angle, generating a low e.m.f. By Position 3, the coil sides are at a right angle to the flux, cutting it at the maximum rate and producing maximum e.m.f. In Position 4, the e.m.f. decreases as the angle changes. At Position 5, the loop is again parallel to the flux, and e.m.f. returns to zero. In Position 6, the sides move under poles of opposite polarity, reversing the direction of the induced e.m.f. The reverse e.m.f. reaches its maximum at Position 7 and returns to zero as it completes the revolution at Position 1.

This process demonstrates that the e.m.f. generated within the loop itself is inherently alternating. This occurs because any specific coil side, such as AB, experiences current in one direction under a North pole and the opposite direction under a South pole. If a load is connected directly to the loop ends, an alternating current would flow. To produce direct current, the alternating voltage must be converted using a device called a commutator, which serves as a mechanical rectifier.

The Commutator and Rectification Process

The function of a commutator is to reverse the connection between the coil sides and the external load at the exact instant the current in the coil side reverses. This ensures the current through the load remains unidirectional. Structurally, the commutator consists of a cylindrical metal ring divided into two halves or segments, labeled C1 and C2, which are separated by a thin sheet of mica for insulation. The commutator is mounted on and insulated from the rotor shaft. Two stationary carbon brushes rest on the commutator to lead the current to the external load. This arrangement ensures the coil side under the South pole is always connected to the positive brush, while the side under the North pole is connected to the negative brush.

During one half-revolution, segment C1 connects coil side AB to the load while segment C2 connects side CD. Current flows through the load in a specific direction (e.g., Q to P). After a 180-degree rotation, the positions and current directions in the coil sides reverse, but the segments C1 and C2 have also rotated. Consequently, the commutator reverses the coil connections to the load such that side AB now connects to point Q and side CD to point P. This keeps the load current flowing from Q to P consistently. While the resulting voltage is direct, it is pulsating rather than steady, varying from zero to maximum twice per revolution. To achieve a steady direct voltage suitable for commercial use, a large number of coils are connected in series to form an armature winding.

Comprehensive Construction of D.C. Machines

D.C. generators and motors share the same general construction, and any d.c. generator can theoretically run as a motor and vice-versa. There are five principal components in all d.c. machines. The first is the field system, which produces a uniform magnetic field. It consists of an even number of salient poles bolted to a circular frame called a yoke, which is usually made of solid cast steel. Pole pieces are made of stacked laminations. Field coils are wound on these poles and carry d.c. exciting current, arranged so adjacent poles have opposite polarity. The resulting magnetic flux passes through the poles, an air gap (typically ranging from $0.5\,mm$ to $1.5\,mm$), the armature, and the frame. Because the armature and field systems have high permeability, most of the magnetomotive force (m.m.f.) is used to set up flux in the air gap; reducing the gap length can reduce the required size of field coils.

The second component is the armature core, which is keyed to the machine shaft. It is made of slotted soft-iron laminations (approximately $0.4\,mm$ to $0.6\,mm$ thick) coated with insulating film to reduce eddy current loss. These laminations are stacked to form a cylinder. The third component is the armature winding, consisting of insulated conductors placed in the core slots. Conductors are connected in series-parallel to increase voltage and current respectively. These form a closed-circuit winding. The fourth component is the commutator, made of copper segments insulated by mica. Great care is taken during its construction because any eccentricity causes brushes to bounce, leading to sparking, which can burn brushes and carbonise the commutator. Finally, carbon brushes are used to maintain electrical contact between the rotating commutator and the stationary load. Brush pressure is managed by adjustable springs; excessive pressure causes overheating, while weak pressure leads to sparking. Multipole machines have as many brushes as poles, with brushes of the same polarity connected to a single terminal.

General Features and Geometry of Armature Windings

In d.c. machines, windings are distributed in slots over the armature circumference. Because every conductor moves at right angles to the magnetic flux, the induced e.m.f. is calculated as follows:

$e = Bvl\text{ volts}$

Where $B$ is the magnetic flux density in $Wb/m^2$, $l$ is the length of the conductor in metres, and $v$ is the velocity of the conductor in $m/s$. These conductors are connected to form coils, which are the basic units of armature windings. A single-turn coil has two conductors (coil sides), while a 4-turn coil has eight coil sides. Coil sides are typically placed a pole span apart (one under a North pole and the other under a South pole) so their e.m.f.s add together. For example, if one conductor induces $2.5\,V$, a single-turn coil induces $5\,V$, and a 4-turn coil induces $20\,V$.

Most d.c. windings are double-layer windings, meaning there are two coil sides per slot. One side lies at the top (given odd numbers) and the other at the bottom (given even numbers). Connections ensure a top coil side is joined to a bottom coil side approximately one pole pitch away. These conductors are connected through commutator segments to form a series-parallel system. All d.c. armature windings must be of the closed type to facilitate commutation.

Technical Terminology of Armature Windings

Several specific terms define the geometry of these windings. The Commutator Pitch ($Y_C$) is the number of commutator segments spanned by each coil; it is always a whole number. Since each coil has two ends and two connections meet at each segment, the number of coils always equals the number of commutator segments. The Pole-Pitch is the distance measured in slots or conductors per pole. For instance, if a 4-pole generator has 16 coils (16 slots), the pole pitch is $16/4 = 4$ slots or $32/4 = 8$ conductors. The Coil Span or Coil Pitch ($Y_S$) is the distance in slots or conductors spanned by a single coil. A Full-Pitched Coil occurs when the coil span equals the pole pitch, resulting in maximum induced e.m.f. with a 0-degree phase difference between coil sides. A Fractional Pitched Coil occurs when the span is less than the pole pitch, which uses less copper but reduces the generated e.m.f.

Additional pitches include the Back Pitch ($Y_B$), the distance between two sides of a coil at the back of the armature, and the Front Pitch ($Y_F$), the distance between coil sides attached to the same commutator segment. The Resultant Pitch ($Y_R$) is the algebraic sum of the back and front pitches, representing the distance between the starts of successive connected coils. Winding may be Progressive ($Y_B > Y_F$ and $Y_C = +1$), where connections progress in the same direction as the coil trace, or Retrogressive ($Y_F > Y_B$ and $Y_C = -1$), where they move in the opposite direction. Retrogressive windings are rarely used as they require more copper.

Simplex Lap Winding Specifications

In a Simplex Lap Winding, the commutator pitch $Y_C$ equals $1$ and the coil span is approximately one pole pitch. Successive coils "overlap" the preceding ones. The following rules apply: both $Y_B$ and $Y_F$ must be odd and nearly equal to the pole pitch, though they differ by 2; they are of opposite signs. Specifically, for progressive winding, $Y_B = Y_F + 2$, and for retrogressive winding, $Y_B = Y_F - 2$. The average pitch is $(Y_B + Y_F) / 2$, which equals the pole pitch ($Z/P$). For the winding to be possible, $Z/P$ must be an even number. A critical conclusion for simplex lap winding is that the number of brushes equals the number of poles, and the number of parallel paths ($A$) also equals the number of poles ($A = P$). Consequently, the e.m.f. generated is the e.m.f. per parallel path, and the total armature current $I_a$ is the number of poles times the current per parallel path.

Simplex Wave Winding Specifications

In a Simplex Wave Winding, the coils are connected so they "wave" forward under successive pole pairs rather than lapping back. The commutator pitch $Y_C$ is approximately equal to two pole pitches. Specifically, the formula for average pitch is:

$Y_A = \frac{Z \pm 2}{P}$

Where $Z$ is the total number of conductors and $P$ is the number of poles. For this to be a whole number, $Z \pm 2/P$ must be an integer. The commutator pitch is given by:

$Y_C = \frac{N_C \pm 1}{P/2}$

Where $N_C$ is the number of commutator segments. In a simplex wave winding, the number of parallel paths ($A$) is always two, regardless of the number of poles ($A = 2$). While only two brushes are technically necessary, a machine may use as many brushes as poles. The winding connects into a single closed circuit after passing around the armature. If the connection falls to the left of the start point, it is retrogressive; to the right, it is progressive.

Practical Considerations: Dummy Coils and Winding Applications

Sometimes, standard armature punchings do not allow for a whole number for $Y_A$ or $Y_C$. In such cases, "dummy coils" or dead coils are used. These coils are inserted into slots to maintain mechanical balance but are not electrically part of the armature winding. For example, in a 4-pole machine with 22 slots (44 conductors), $Y_A$ would be $11.5$ or $10.5$. By making one coil a dummy (reducing to 42 active conductors), $Y_A$ becomes a whole number ($11$ or $10$), allowing the machine to be wound. One end of the dummy coil is taped, and the other is connected to an unused segment for appearance.

Regarding applications, wave windings are typically used in small machines or low-current armatures because they provide higher terminal voltage by having more conductors in series. Lap windings are used in large machines or high-current armatures because they provide more parallel paths to share the current load. Generally, high-current armatures are lap-wound, and low-current armatures are wave-wound.

Multiplex Windings and Commutation Dynamics

Multiplex windings are used to increase the number of parallel paths beyond what simplex windings allow. The number of paths depends on the "plex" or degree of multiplicity. For a lap winding, $A = P \times \text{plex}$. Thus, a duplex lap winding has $2P$ paths. For a wave winding, $A = 2 \times \text{plex}$, meaning a duplex wave winding has 4 paths regardless of the number of poles. This allows the armature to carry higher total current at lower voltages.

Commutation is the process of reversing the current in an armature coil as it passes a brush while being short-circuited. Good commutation is defined as being "sparkless." If the current hasn't completely reversed when the brush breaks contact with a segment, sparking occurs. To ensure sparkless commutation, brushes should be placed at neutral points where no voltage exists between segments—specifically at the Magnetic Neutral Axis (M.N.A.), where conductors cut zero flux.

Derivation of the E.M.F. Equation

To derive the generated e.m.f. ($E_g$) of a d.c. generator, let $\phi$ be the flux per pole in Webers, $Z$ the total conductors, $P$ the poles, $A$ the parallel paths, and $N$ the speed in r.p.m. The flux cut by one conductor in one revolution is $d\phi = P\phi$. The time for one revolution is $dt = 60/N$ seconds. The e.m.f. generated per conductor is:

$\frac{d\phi}{dt} = \frac{P\phi}{60/N} = \frac{P\phi N}{60}$

The total e.m.f. of the generator is the e.m.f. per parallel path:

$E_g = \frac{P\phi ZN}{60A}$

For wave winding, $A = 2$; for lap winding, $A = P$. Armature resistance ($R_a$) includes the resistance of the winding and the brushes, and is generally less than $1\,\Omega$ in machines except for very small ones.

Classification of D.C. Generators by Excitation

Generators are classified by how their field magnets are excited. Separately Excited Generators have field windings supplied by an independent external d.c. source, like a battery. Output voltage depends on speed and field current ($E_g = P\phi ZN / 60A$). In these, armature current $I_a$ equals load current $I_L$, and terminal voltage $V = E_g - I_a R_a$. Self-Excited Generators use their own output to supply the field winding. These include:

1. Series Generators: Field winding is in series with the armature. It uses a few turns of thick wire. $I_a = I_{se} = I_L$. Terminal voltage $V = E_g - I(R_a + R_{se})$.
2. Shunt Generators: Field winding is in parallel with the armature. It uses many turns of fine wire. Shunt field current $I_{sh} = V/R_{sh}$ and $I_a = I_L + I_{sh}$. Terminal voltage $V = E_g - I_a R_a$.
3. Compound Generators: These have both series and shunt windings. A Short Shunt has the shunt field in parallel only with the armature ($I_{se} = I_L$), while a Long Shunt has the shunt field in parallel with both the armature and series field ($I_{se} = I_a = I_L + I_{sh}$).

Analysis of Losses in D.C. Machines

Losses in d.c. machines appear as heat and lower efficiency. They are categorized into three types:

1. Copper Losses: These result from currents in windings ($I^2 R$). This includes armature copper loss ($I_a^2 R_a$), shunt field copper loss ($I_{sh}^2 R_{sh}$), and series field copper loss ($I_{se}^2 R_{se}$). Brush contact loss is usually grouped here.
2. Iron or Core Losses: These occur in the armature due to rotation in the magnetic field. Hysteresis loss occurs because magnetism in the iron reverses as it passes poles; it is calculated by the Steinmetz formula ($P_h = \eta B_{max}^{1.6} f V$). Silicon steel is used to reduce this. Eddy current loss results from circulating currents in the core; it is reduced by laminating the core ($P_e = K_e B_{max}^2 f^2 t^2 V$), as loss depends on the square of lamination thickness ($t$).
3. Mechanical Losses: These include friction (bearings/brushes) and windage (air friction). Iron and mechanical losses are collectively called "stray losses."

Losses are further categorized as Constant Losses (iron, mechanical, and shunt field losses) or Variable Losses (armature and series field copper losses).

Efficiency Stages and Optimization Conditions

Power stages in a d.c. generator move from Mechanical Power Input ($A$) to Iron and Friction Losses, then to Generated Electrical Power ($E_g I_a$ or point $B$), then to Copper Losses, and finally to Output Power ($V I_L$ or point $C$). Mechanical efficiency is $\eta_m = B/A$, electrical efficiency is $\eta_e = C/B$, and commercial (overall) efficiency is $\eta_c = C/A = \eta_m \times \eta_e$. Commercial efficiency is defined as $\frac{\text{output}}{\text{output + losses}}$.

Efficiency is not constant and varies with the load. For a shunt generator, the efficiency is maximum when the denominator of the efficiency equation is minimized. Mathematically, this occurs when:

$\text{Variable loss} = \text{Constant loss}$

Or specifically, $I_L^2 R_a = W_C$, where $W_C$ represents constant losses. The load current for maximum efficiency is calculated as:

$I_L = \sqrt{\frac{W_C}{R_a}}$

This confirms that a d.c. generator operates at peak efficiency when the load current results in variable losses equal to the constant losses of the machine.