Electrical Machines - DC & AC

DC Machines

• Electrical Machines include DC Generators and DC Motors.

DC Generators

• There are two types of DC Generators.

DC Motors

• Classified into two main types:

  • Separately excited DC motor

  • Self-excited DC motor, which includes:

    • DC series motor

    • DC shunt motor

    • DC compound motor

Construction of DC Machines

• The construction is the same for both DC motors and DC generators, consisting of:

  • Yoke or Magnetic frame

  • Pole core and pole shoes

  • Field winding

  • Armature core and windings

  • Commutators

  • Brushes

  • Bearings

  • End Covers

  • Shaft

1. Yoke or Magnetic Frame

• It is the outer frame of the DC machine.

• Provides mechanical support to the pole core and pole shoes.

• Made of cast steel in large machines and cast iron in smaller machines.

• Functions:

  • Provides support to the pole core and pole shoe.

  • Offers a low reluctance path for the magnetic flux.

  • Protects the inner parts of the machine.

2. Pole Core and Pole Shoes

• Fixed to the magnetic frame (yoke) using bolts.

• Made of thin cast steel or cast iron, often with laminations.

• Functions:

  • The pole core carries the field winding.

  • The pole shoe enlarges the area for the armature core to encounter magnetic fluxes and gives a particular shape.

3. Field Winding

• Exciting winding placed on the pole core to produce the required magnetic field.

• Requires a relatively small DC power to generate a strong magnetic field.

• Wound on all pole cores in a series connection.

4. Armature Core and Windings

• The rotating component of the DC motor is called the "Armature".

• Consists of a laminated cylinder called the "Armature core" placed over the shaft.

• Functions:

  • Provides a place for conductors in slots.

  • Offers a low reluctance path for the magnetic flux.

  • Made of silicon steel material.

• Armature windings are made up of insulated conductors (typically copper wire) placed in the armature slots.

• Two types of armature windings:

  • Lap winding

  • Wave winding

5. Commutators

• Cylindrical, wedge-shaped hard-drawn copper bars or segments that rotate with the armature.

• Functions:

  • Collects current from armature conductors and supplies current to them.

  • Converts alternating current (AC) to direct current (DC) in generators.

  • Converts direct current (DC) to alternating current (AC) in motors.

6. Brushes

• A set of carbon brushes attached to the rotating armature via the commutator, connecting to the external circuit.

• The main purpose is to tap the electrical power generated in the rotating machine.

7. Bearings

• High carbon steel ball or roller bearings are fitted to ensure smooth rotation and reduce frictional losses.

8. End Covers

• Components attached to the yoke ends that provide support to the bearings.

9. Shaft

• Made of mild steel with maximum breaking strength.

• Transfers mechanical power to mechanical loads.

Working Principle of DC Motors

• Motors operate based on the Lorentz principle:

  • Whenever a current-carrying conductor is placed in a magnetic field, it experiences a mechanical force (torque) and starts to rotate.

• Consider a 2-pole (N & S) setup with a conductor carrying current (I) placed in the magnetic field.

• When field windings on the poles are excited by a DC source, the poles become magnetized, producing a strong magnetic field.

• The conductor, when placed in this field, creates its own (weaker) magnetic field.

• The interaction between these two fields produces a resultant field.

• This resultant field causes the rotation of the armature conductor. The direction can be found using Fleming's Left Hand Rule (FLHR).

• The working of a DC motor can be explained by the DC motor's Magnetomotive Force (MMF) developed by these two magnetic fields.

• If the DC motor has 'Z' number of conductors and produces a resultant flux, it causes MMF, which develops a resultant force ($F_r$) that rotates the armature conductors.

• The electromagnetic torque developed in the armature conductors will be continuous if the direction of current in each conductor changes when it crosses the Magnetic Neutral Axis (MNA).

• This reversal of current direction is achieved using a commutator, which helps in developing continuous torque.

• MNA → Magnetic Neutral Axis

• GNA → Geometrical Neutral Axis

Back EMF in a DC Motor

• When a DC source excites the armature conductor placed in the main magnetic field, electromagnetic torque is developed, causing the motor to rotate.

• Due to armature rotation, the armature conductors cut the magnetic flux of the main magnetic field, inducing an EMF in the armature conductors.

• This induced EMF opposes the cause and is called "Back EMF" ($E_b$).

• The magnitude of back EMF is given by: $E_b = fraction{\phi Z N P}{60 A}$ where:

  • $\phi$ = Magnetic flux

  • Z = Total no. of conductors

  • N = Speed of motor

  • P = No. of poles

  • A = No. of parallel paths

    • A = P for lap winding

    • A = 2 for wave winding

Equivalent Circuit of a DC Motor

• In a DC motor, current flows from the line into the armature against the generated voltage. Using Kirchhoff's Voltage Law (KVL):
  $V = E<em>b + I</em>a R<em>a + V</em>b$

• If the drop across the brushes is negligible:
  $V = E<em>b + I</em>a R_a$

• Multiplying by $I<em>a$: $VI</em>a = E<em>b I</em>a + I<em>a^2 R</em>a$

• $E<em>b = V - I</em>a R_a$ where:

  • $P<em>i = VI</em>a$ = Input power

  • $P<em>m = E</em>b I_a$ = Mechanical power

  • $P<em>c = I</em>a^2 R_a$ = Copper loss in the armature

Characteristics of Separately Excited DC Motors

• Types of Characteristics:

  • Torque ($T<em>a$) and Armature current ($I</em>a$)

  • Speed (N) and Armature Current ($I_a$)

  • Torque ($T_a$) and Speed (N)

  • Electrical characteristic (Torque ($T<em>a$) and Armature current ($I</em>a$))

  • Mechanical characteristic (Speed (N) and Armature Current ($I_a$))

• Relations:

  • $T = 9.55 \times \frac{E<em>b I</em>a}{N}$

  • $T<em>a \propto I</em>a$

  • $E_b = \frac{\phi Z N P}{60 A}$

  • $N \propto \frac{V - I<em>a R</em>a}{\phi}$

1. Torque ($T<em>a$) vs. Armature Current ($I</em>a$) Characteristics

• Since the field winding is excited by a constant supply voltage 'V', the field current ($I_{sh}$) is constant.

• Therefore, torque is constant with a change in armature current ($I<em>a$), i.e., $T</em>a \propto I_a$

2. Speed (N) vs. Armature Current ($I_a$) Characteristics

• $N \propto E<em>b \implies N \propto V - I</em>a R_a$

• When $I<em>a$ increases, the '$I</em>a R_a$' drop increases, so speed decreases, resulting in a drooping characteristic.

3. Torque ($T_a$) vs. Speed (N) Characteristics

• From the torque equation:
  $T_a \propto \frac{1}{N}$

Speed Control of DC Motors

• The speed equation of a DC motor is:
  $N = \frac{V - I<em>a R</em>a}{\phi} \times \frac{60A}{P}$

• $N \propto \frac{V - I<em>a R</em>a}{\phi}$

• Methods for speed control of DC shunt motors include:

  • Armature Resistance Control method

  • Flux control method

  • Applied voltage control method

1. Armature Resistance Control Method

• A series resistance ($R_s$) is connected to the motor to control its speed.

• From $N \propto (V - I<em>a R</em>a)$, when $R<em>a$ increases, $I</em>a$ decreases, which reduces the speed.

2. Flux Control Method

• Used to control the speed of a DC shunt motor above its rated speed by reducing the field flux.

• Since $N \propto \frac{1}{\phi}$, a variable resistance element (shunt field rheostat) is connected in series with the shunt field winding.

3. Applied Voltage Control Method

• Two voltage control methods are:

  • Multiple voltage control

  • Ward-Leonard System

i. Multiple Voltage Control

• The field winding receives a constant supply voltage, while the armature winding receives a variable voltage, achieved using a switch-gear.

• $N \propto V$

ii. Ward-Leonard System

• An arrangement to control the speed of a DC shunt motor.

• Motor M2’s speed is controlled. M1 (AC or DC motor) runs at a constant speed and is coupled to generator "G".

• The output of G feeds into the armature of motor M2. The field winding of M2 gets a constant DC supply voltage.

• By varying the generator's output, the supply voltage to M2’s armature can be varied. The generator output can be controlled using a field regulator, allowing smooth speed control.

Three-Phase Induction Motors

Construction

• Consists of two main parts:

  • Stator: Stationary part with three-phase windings.

  • Rotor: Rotating part connected to the mechanical load via a shaft.

1. Stator

• Laminated construction made of stampings (0.4 to 0.5mm thick).

• Stampings are slotted to carry the stator winding and are insulated to minimize iron losses.

• Multiple stampings are stacked to build the stator core.

• The slots carry a three-phase winding, connected in star or delta, wound for a definite number of poles.

• Radial ducts are provided for cooling.

2. Rotor

• Placed inside the stator with an air gap of 0.4mm to 4mm.

• Two types:

  • Squirrel cage rotor

  • Slip ring or phase wound rotor

a. Squirrel Cage Rotor

• Cylindrical core with slots on its periphery.

• Consists of uninsulated copper or aluminum bars (rotor conductors) placed in the slots.

• Bars are shorted at each end with conducting copper end rings, usually brazed for mechanical strength.

• The entire structure looks like a cage, forming a closed electrical circuit.

b. Slip Ring Rotor (or Phase Wound Rotor)

• Rotor winding is similar to the stator winding.

• Wound for the same number of poles as the stator and carries a three-phase star or delta connected, distributed winding.

• Laminated and slotted construction.

• The three ends of the three-phase winding are connected to slip rings.

• External resistances can be added in series with each phase of the rotor winding through slip rings.

• In running condition, the slip rings are shorted.

Working Principle

• Works on the principle of electromagnetic induction.

• When a three-phase supply is given to the stator winding, a rotating magnetic field of constant magnitude is produced.

• The speed of this rotating magnetic field is the synchronous speed ($N<em>s$) in r.p.m., given by: $N</em>s = \frac{120f}{P}$
  where f = frequency and P = number of poles.

• This rotating field produces an effect of rotating poles around the rotor.

• The rotor is initially stationary, so there is a relative motion between the rotating magnetic field (RMF) and rotor conductors.

• An electromotive force (EMF) gets induced in the rotor conductors (rotor induced EMF) whenever the conductor cuts across the flux.

• Since the rotor forms a closed circuit, the induced EMF circulates a rotor current.

• Any current-carrying conductor produces its own flux, so the rotor produces its own (rotor flux).

• The stator flux and the rotor flux interact.

• On one side of the rotor conductor, the fluxes are in the same direction (high flux area),

• While on the other side they cancel each other (low flux area).

• The high flux density area exerts a push on the rotor conductor toward the low flux density area due to the interaction of the two fluxes.

• As all rotor conductors experience a force, the rotor experiences a torque and starts rotating.

• According to Lenz's law, the direction of the induced current in the rotor opposes the cause producing it.

• The cause of the rotor current is the induced EMF due to the relative motion between the rotating magnetic field and the rotor conductors.

• To oppose the relative motion, the rotor experiences a torque in the same direction as the rotating magnetic field and tries to catch up with its speed.

Slip of Induction Motor

• The difference between the speed of the rotating magnetic field and the actual rotor speed is called slip speed:
  $N_s - N = \text{slip speed}$

• The slip (s) is defined as the difference between the synchronous speed ($N<em>s$) and actual rotor speed (N), expressed as a fraction of the synchronous speed: $s = \frac{N</em>s - N}{N<em>s}$ $s\% = \frac{N</em>s - N}{N_s} \times100$

Torque Equation

• The torque (T) developed by the rotor is directly proportional to:

  • Rotor current ($I_2$)

  • Rotor EMF ($E_2$)

  • Power factor of the rotor circuit ($\cos{\phi<em>2}$) $T \propto E</em>2 I<em>2 \cos{\phi</em>2}$

• Rotor Current:
  $I<em>2 = \frac{sE</em>2}{Z<em>2} = \frac{sE</em>2}{\sqrt{R<em>2^2 + (sX</em>2)^2}}$

• Rotor Power Factor:
  $\cos{\phi<em>2} = \frac{R</em>2}{Z<em>2} = \frac{R</em>2}{\sqrt{R<em>2^2 + (sX</em>2)^2}}$

• Torque Equation:
  $T = k \frac{sE<em>2}{\sqrt{R</em>2^2 + (sX<em>2)^2}} \frac{R</em>2}{\sqrt{R<em>2^2 + (sX</em>2)^2}} = \frac{k s E<em>2^2 R</em>2}{R<em>2^2 + (sX</em>2)^2}$

Starting Torque

• At starting, s = 1; $sE<em>2 = E</em>2$ and $sX<em>2 = X</em>2$
  $T<em>s = k \frac{E</em>2^2 R<em>2}{R</em>2^2 + X_2^2}$

• If the stator supply voltage (V) is constant, the flux set up by the stator is fixed, and therefore, the induced EMF in the rotor ($E<em>2$) is constant. $T</em>s = \frac{k<em>1 R</em>2}{R<em>2^2 + X</em>2^2}$

Condition for Maximum Starting Torque

• To find the condition for maximum starting torque, differentiate the torque equation with respect to $R<em>2$ and equate to zero. $\frac{dT</em>s}{dR<em>2} = 0$ $\frac{d}{dR</em>2} \left( \frac{k<em>1 R</em>2}{R<em>2^2 + X</em>2^2} \right) = 0$
  $k<em>1 \frac{(R</em>2^2 + X<em>2^2) - R</em>2(2R<em>2)}{(R</em>2^2 + X<em>2^2)^2} = 0$ $R</em>2^2 + X<em>2^2 - 2R</em>2^2 = 0$
  $X<em>2^2 = R</em>2^2$
  $R<em>2 = X</em>2$

• Thus, the starting torque will be maximum when:
  Rotor Resistance / phase = Standstill Rotor Reactance

Torque-Slip Characteristics

• The torque-slip characteristics are divided into three regions:

  • Low slip region (Lightly loaded conditions)

  • Medium slip region

  • High slip region (Fully loaded conditions)

1. Low Slip Region

• Rotor speed (Nr) is almost equal to the synchronous speed of the rotating magnetic field (Ns).

• Slip s ≈ 0.

• $T<em>s = k \frac{s E</em>2^2 R<em>2}{R</em>2^2 + (sX_2)^2}$

• As s approaches 0, $T \propto s$

2. Medium Slip Region

• Torque attains a maximum value when $R<em>2 = X</em>2$.

3. High Slip Region

• Rotor speed Nr << Ns.

• slip value increases from 0 to 1.

• So $T \propto \frac{1}{s}$

Application of Induction Motors

• Squirrel cage induction motors have moderate starting torque and constant speed characteristics.

• They are preferred for driving fans, water pumps, grinders, lathe machines, printing machines, and drilling machines.

• Slip ring induction motors have high starting torque, making them ideal for lifts, hoists, elevators, cranes, and compressors.

Losses

• The various losses taking place in three-phase induction motors are:

  • Stator losses: These include copper losses and iron losses.

  • Rotor losses: In running condition rotor frequency is very small, hence iron losses are negligible, only rotor copper losses are considered.

  • Mechanical losses: These include friction and windage losses.

  • $P<em>{\text{out}} = P</em>m - \text{Mechanical losses}$

Types of Single-Phase Induction Motors

• Depending upon the methods of producing rotating stator magnetic flux, the single-phase induction motors are classified as:

  • Split-phase induction motor

  • Capacitor-start induction motor

  • Capacitor-start capacitor-run induction motor

  • Shaded-pole induction motor

1. Split-Phase Induction Motor

• This type of motor has a single-phase stator winding called the main winding.

• In addition to this, the stator carries one more winding called the auxiliary winding (or) starting winding.

• The auxiliary winding carries a series resistance such that its impedance is highly resistive in nature.

• The main winding is inductive in nature.

• Let $I_m$ = current through the main winding,

• $I_{st}$ = current through auxiliary winding.

• As the main winding is inductive, current $I<em>m$ lags voltage V by a large angle $$\phim$, while$I_{st}$is almost in phase with V as the auxiliary winding is highly resistive.</p></li><li><p>Thus, there exists a phase difference of$$\alpha$ between the two currents and hence between the two fluxes produced by the two currents.

• The resultant of these two fluxes is a rotating magnetic field.

• Due to this, the starting torque which acts only in one direction is produced to make the motor self-starting.

• The auxiliary winding has a centrifugal switch in series with it.

• When the motor gathers a speed of up to 75 to 80% of synchronous speed, the centrifugal switch opens mechanically, and in running condition, the auxiliary winding remains out of the circuit.

• So, the motor runs only on the stator winding.

Applications

• These motors have low starting current and moderate starting torque.

• They are used for easily started loads like fans, blowers, grinders, centrifugal pumps, washing machines, oil burners, office equipment, etc.

2. Capacitor-Start Single-Phase Induction Motor

• A capacitor is connected in series with the auxiliary winding.

• The current $I<em>m$ lags the voltage by angle $$\phim$, while due to the capacitor, the current$I{st}$leads the voltage by angle$$\phi</em>{st}$.

• Hence, there exists a large phase difference between the two currents, which is almost 90°, which is an ideal case.

• The starting torque is proportional to '$I_m$' and hence such motors produce very high starting torque.

• When the speed approaches 75 to 80% of the synchronous speed, the starting winding gets disconnected due to the operation of the centrifugal switch.

• The capacitor remains in the circuit only at start; hence, it is called capacitor-start motors.

• In case of capacitor-start capacitor-run motor, there is no centrifugal switch, and the capacitor remains permanently in the circuit. This improves the power factor.

• The starting torque available in such a type of motor is about 50 to 100% of full load torque.

Applications

• These motors have high starting torque and hence are used for hard starting loads.

• These are used for compressors, conveyors, grinders, fans, blowers, refrigerators, air conditions, etc.

• These are the most commonly used motors.

• The capacitors start capacitor-run motors are used in ceiling fans, blowers, and air-circulators.

3. Shaded Pole

• This type of motor consists of a squirrel cage rotor and a stator consisting of salient poles (i.e., projected poles).

• The poles are shaded, i.e., each pole carries a copper band on one of its unequally divided parts called the shading band.

• The current carried by the stator winding is alternating and produces alternating flux.

• At instant t 1, the rate of rise of current and hence the flux is very high.

• Due to the transformer action, large EMF gets induced in the copper shading band.

• This circulates current through the shading band as it is short-circuited, Producing its own flux.

• According to Lenz's law, the direction of its current opposes the cause (i.e., rise in current).

• Hence, there is crowding of flux in the non-shaded part while weakening of flux in the shaded part; overall magnetic axis shifts in the nonshaded part.

• At instant t2, the rate of rise of Current and hence the rate of change of flux is almost zero.

• Hence, there is very little induced EMF in the shading ring.

• Hence, the shading ring flux is also negligible.

• Hence, the main flux distribution is uniform, and the magnetic axis lies at the center of the pole face.

Applications

• These motors are cheap but have very low starting torque, low Power factor, and low efficiency.

• These motors are commonly used for small fans, toy motors, advertising displays, film projections, record players, gramophones, hair dryers, photocopying machines, etc…

Synchronous Generators (Alternators)

Construction

• In synchronous generators (alternators), the stationary winding is called the 'stator' while the rotating winding is called the 'rotor'.

1. Stator

• The stator is a stationary armature.

• It consists of a core and slots to hold the armature winding.

• The stator core uses a laminated construction.

• It is built up of special steel stampings insulated from each other with Varnish or paper.

• The laminated construction is basically to keep down eddy current losses.

• The entire core is fabricated in a frame made of steel plates.

• The Core has slots on its periphery for housing the armature Conductors.

• Ventilation is maintained with the help of holes cast in the frame

2. Rotor

• There are two types of rotors used in alternators:

  • Salient pole (projected pole type)

  • Smooth cylindrical or non-salient type

i. Salient Pole (Projected Pole Types)

• Also called projected pole type, as all the poles are Projected out from the surfaces of the rotor.

• The poles are built up of thick steel laminations.

• The poles are bolted to the rotor.

• The pole face has been given a specific shape.

• The field winding is provided on the pole shoe.

• These rotors have large diameters and small axial lengths.

• As the mechanical strength of the salient pole type is less, this is Preferred for low-speed alternators ranging from 125 rpm to 500 rpm

• The prime movers used to drive such rotors are generally water turbines and IC engines.

ii. Smooth Cylindrical or Non-Salient Type

• Also called non-salient type (or) non-projected pole type of rotor.

• The rotor consists of a smooth solid steel cylinder having numbers of slots to accommodate the field coil.

• The slots are covered at the top with the help of steel (or) manganese wedges.

• The unslotted portions of the cylinder itself act as the poles.

• The poles are not projecting out, and the surface of the rotor is smooth, which maintains uniforms air gaps between stator and the rotor.

• These rotors have small diameters and large axial lengths.

• This is to keep the peripheral speed within limits.

• The main advantage of this type is that these are mechanically very strong and thus preferred for high-speed alternators ranging between 1500 to 3000 rpm.

• Such high-speed alternators are called turbo alternators!

• The prime movers used to drive such types of rotors are generally steam turbines, and electric motors.

Working Principle of Alternators

• Synchronous generators work on the principle of electromagnetic induction.

• When there is relative motion between the conductors and the flux, EMF gets induced in the Conductors.

• Consider the relative motion of a single conductor under the magnetic field produced by two stationary poles.

• The magnetic axis of the two poles produced by the field is vertical.

• Let the conductor start rotating from position 1. At this instant, the entire velocity component is parallel to the flux lines.

• Hence, there is no cutting of them lines by the conductor. Hence induced EMF in the conductor is also Zero.

• As the conductor moves from position 1 towards position 2, part of the velocity component becomes perpendicular to the flun lines. Proportional to that, EMF gets induced in the conductor.

• The magnitude of such an induced EMF increases as the conductor moves from position I towards 2.

• At Position 2, the entire velocity component is perpendicular to the flux lines.

• Hence, there exists maximum cutting of the flux lines, and at this instant, the induced Emmit in the conductor is at its maximum.

• As the position of the conductor changes from 2 towards. 3, the velocity component decreases perpendicular to the flux starts, And hence induced emf magnitude also starts decreasing. At Position 3, again the entire velocity component is parallel to the flum lines.

• Hence, at this instant, induced emf in the Conductor is zero.

• As the conductor moves from position 3 towards 4, the Velocity component perpendicular to the flux lines again starts increasing.

• But the direction of the velocity component now is Opposite to the direction of the velocity component existing during the Movement of the conductor from position 1 to 2.

• Hence, an induced emf in the conductor increases but in the opposite Direction.

• At Position 4, it achieves maxima in the opposite direction, As the entire velocity component becomes perpendicular to the flun lines.

• Again from position 4 to 1, induced cf decreases, and finally, At position 1 again becomes zero. This cycle continues as the conductor rotates at a certain speed.

• So if we plot the magnitudes of the induced e.m-t against The time, we got an alternating nature of the induced em-f as above.

• For a 4-pole alternator, one mechanical revolution corresponds To one electrical cycle (360° electrical) of an induced EMF.

• In a 4-pole alternator, for one revolution of the conductor, We get two electrical cycles of the induced EMF due to Flux distribution due to 4 poles.

• In general, one mechanical revolution of rotor = I cycles of Emf Electrically.

• As speed is N rpm, in one second, the rotor will complete (N/60) revolutions.

• But electrical cycles/sec = Frequency = f

• Frequency f = (No. of electrical cycles per revolution) X (No. of revolutions per second)
  $f = \frac{P}{2} \times \frac{N}{60} = \frac{PN}{120} \text{ Hz (Cycles per sec)}$

• So there exists a fixed relationship between three quantities,

• the number of poles p, the speed of the rotor N in rpm, and

• the frequency of an induced Emmit in the Hertz.

• The speed of the alterna for at which it produces induced EMF at the rated frequency for numbers of poles is called Synchronous speed Ns.
  $N_s = \frac{120f}{P}$
  where f = Required rated frequency.

Example

• A 12-pole alternator is coupled to an engine running at 500 rpm.

• It supplies a 3-phase induction motor having full load Speed at 1440 rpm.

• Find t. slip and number of poles of the motor.