For a dc motor from the power equation, it is known that,

Pm = Gross mechanical power developed = EbIa = VIa - Ia2Ra

Where,

V = Applied voltage

Eb = Back emf

Ia = Armature current

Ra = Armature resistance

For maximum Pm,

$\begin{array}{l}\frac{d{P}_m}{d{I}_a}=0\\ \Rightarrow 0=V-2I_a{R}_a\\ \Rightarrow I_a{R}_a=\frac{V}{2}\end{array}$

Substituting in voltage equation (V = Eb + IaRa), we get

$\begin{array}{l}V=E_b+I_a{R}_a=E_b+\left(\frac{V}{2}\right)\\ \Rightarrow E_b=\frac{V}{2}\end{array}$

So that when a DC motor generates maximum power, ratio of applied voltage to back emf is 2 : 1

In a DC motor, the back emf is directly proportional to speed and flux.

Eb ∝ Nϕ

Where N is speed and ϕ is flux.

In a DC shunt motor, flux is constant.

So, the back emf is directly proportional to speed.

Armature resistance control:

We know that,

$N\propto \frac{E_b}{\varphi }$

$N\propto \frac{V-I_a\left(R_a+R\right)}{\varphi }$

We can control the speed by increasing armature resistance. This method gives only below base speeds. This method is a constant torque and variable power drive.

Field control method:

We know that,

$N\propto \frac{E_b}{\varphi }$

$N\propto \frac{V-I_a{R}_a}{\varphi }$

By varying flux, we can increase the speed more than its base speed. This method is constant power and variable torque drive.

Wave winding:

• In wave winding, the number of parallel paths is two
• This winding is mainly used for high voltage and low current applications

Lap winding:

• In lap winding, the number of parallel paths (A) is the same as the number of brushes and poles
• This winding is mainly used for low voltage and high current applications

Explanation:

A starter is necessary to start a DC motor because it restricts initial high armature current that exists, as the value of starting back-EMF is zero.

A resistor is used in the starter for a DC shunt motor

• When the connected dc motor is to be started, the lever is turned gradually to the right
• When the lever touches point 1, the field winding gets directly connected across the supply, and the armature winding gets connected with resistances R1 to R5 in series
• During starting, full resistance is added in series with the armature winding
• Then, as the lever is moved further, the resistance is gradually is cut out from the armature circuit
• Now, as the lever reaches to position 6, all the resistance is cut out from the armature circuit and armature gets directly connected across the supply

 So, the purpose of including an external resistance at the time of starting a DC motor is to reduce the starting current.

• Coils are typically wound with enameled copper wire, sometimes termed magnet wire.
• The winding material must have a low resistance, to reduce the power consumed by the field coil, but more importantly to reduce the waste heat produced by ohmic heating.
• The enameled wire basically refers to an aluminium or copper wire which has been given a coating.
• This thin layer of insulation mates it useful for building transformers, motor, inductors, hard disk actuators, speakers, electromagnets, etc.
• The enameled copper wire is electrolytic – refined copper.
• Since these wires come with a coating they are also popularly called magnet wires.
• This type of copper wire is most extensively used in constructing transformers and motors.
• It finds use in the application which needs insulated wires that are tightly coiled.
• The main reason for using this coating or ‘enamel’ is to prevent the wire from getting caught in accidental short circuits.
• The enameled copper wire is also useful because it can be soldered easily.
• Magnet wires will produce electromagnetic fields if one winds them to create coils; these get reenergized in the process.
• The enameled copper wire is used to convert electrical energy to mechanical energy for making motors, office HVAC, etc.
• The main reason for using copper is because of its high electrical conductivity.
• So the use of this metal (Cu) as compared to other types of metals is more because it improves energy efficiency for motors.
• Thus enameled copper wire is used for generator, motor winding, and field windings.

The voltage regulation of a generator is defined as the change in the voltage drop from no load to full load to full load voltage.

Voltage regulation = (no-load voltage - full load voltage) / full load voltage

Ideally DC generators should have zero voltage regulation.

In the case of a series generator, the field is connected in series with the armature. Any increase in load current causes an increase in the field and hence the terminal voltage rises.

Hence it has negative voltage regulation and it has the poorest voltage regulation.

During on-load conditions, differentially compounded DC generator has the poorest voltage regulation.

During the no-load condition, the DC series generator has the poorest voltage regulation.

Open circuit test:

• It is done by keeping one of the windings open (without load, usually high voltage winding is open) and applying rated voltage to other winding (usually low voltage winding because it is easier to apply rated voltage).
• The current drawn from this terminal is the no-load current at low power factor corresponding to the core loss component. Since the no-load current is very small it doesn’t contribute to the copper loss. Core loss is calculated by multiplying the applied voltage and no-load current.
• As the secondary side is open, the entire coil will be purely inductive in nature. So, the power will be lagging due to the inductive property of the circuit. So LPF (Low Power Factor) Wattmeter is used in the open circuit test of the transformer.

It is used to find

• The core loss of the transformer
• The no-load current
• Equivalent resistance referred to metering side
• Shunt branch parameters i.e. magnetizing impedance

Short circuit test:

• It is done by shorting one of the winding terminals (usually low voltage terminal) and applying a small voltage across the other winding terminals (high voltage terminal because the current in HV terminal will be less and easy to handle) and using a wattmeter to measure the power dissipated in the LV terminal. Wattmeter will indicate the full load copper loss.
• In the short circuit test, the secondary winding of the transformer is short-circuited. As the secondary side is short-circuited the entire coil will be purely resistive in nature. So, the power factor will be High or unity.

Short circuit test is done to find

• The full load copper loss or ohmic loss
• Short circuit current

Per unit system:

It is usual to express voltage, current, voltamperes and impedance of an electrical circuit in per unit (or percentage) of base or reference values of these quantities.

The Per Unit value of any quantity is defined as

PU value = actual value/base value

Per unit system in transformers:

The per unit impedance of a transformer is the same whether computed from primary or secondary side so long as the voltage bases on the two sides are in the ratio of transformation (equivalent per phase ratio of a three-phase transformer which is the same as the ratio of line-to-line voltage rating).

Transformation ratio of transformer is given by K = V2/V1 = E2/E1 = N2/N1.

Where N1 is the number of primary turns

V1 is the primary voltage

N2 is the number of secondary turns

V2 is the secondary voltage

• Ferrite core is a type of magnetic core made of ferrite on which the windings of electric transformers and other wound components such as inductors are formed.
• It is used for high-frequency applications for its properties of high magnetic permeability coupled with low electrical conductivity (high resistance)
• It helps in preventing eddy currents

The difference between the iron core and ferrite core inductors:

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Important Points:

• The transformer core is normally made up of silicon steel.
• For low-frequency operations, the core used is made up of silicon iron.
• For high-frequency operations, the ferrite core is used.

• In a transformer, primary volt-ampere is equal to secondary volt-ampere and primary ampere-turns are also equal. So, EMF per turn in both the winding are equal.
• Total induced emf on both sides depends on the number of turns, flux, and frequency.
• If a number of turns on the secondary more than the primary, then emf induced in the secondary will more than the primary side and vice versa, but the emf per turn in both the winding are equal.

Note:

The turn ratio for the transformer is given by

$\frac{V_p}{V_s}=\frac{I_s}{I_p}=\frac{N_p}{N_s}$

∴ $\frac{V_p}{N_p}=\frac{V_s}{N_s}$

So that emf induced per turn in the primary winding is equal to the emf induced per turn in the secondary winding.

Where, 

Vp = voltage on the primary side

Vs = voltage on the secondary side

Ip = current on primary side

Is = current on the secondary side

Np = turns on the primary side

Ns = turns on the secondary side

Concept:

Turn ratio (n) of a transformer is given as

$n=\frac{N_1}{N_2}=\frac{E_1}{E_2}=\frac{I_2}{I_1}$

Where,

N1 = Number of turns across primary side

N2 = Number of turns across secondary side

E1 = Primary side voltage

E2 = Secondary side voltage

I1 = Primary current

I2 = Secondary current

Calculation:

Given-

N₁ = 200, N₂ = 50, E₁ = 240 V

∴ $\frac{200}{50}=\frac{240}{E_2}$

E₂ = 60 V

Slip (s):

In the induction motor, the rotor rotates with a speed of N slightly less than the synchronous speed (N_s). It slips the speed by a value is called slip speed.

Formula:

The slip speed can be calculated as

s = N_s - N

The percentage of the slip is calculated as 

$s=\frac{N_s-N}{N_s}\times 100$

The rotor frequency is f' = s f.

f = Supply frequency

Calculation:

Given that,

Supply frequency f = 50 Hz

At no-load, a voltmeter is connected on the rotor side. 

120 pulsations per minute i.e., (120 / 60) = 2 cycles /sec.

Voltmeter makes one cycle in the positive half cycle(emf is positive) and one cycle in the negative half cycle (emf is negative).

i.e., Two cycles in voltmeter = One cycle in rotor emf

∴ The frequency of the rotor is

f' = 1 cycle per second = 1 Hz

The rotor frequency is f' = s f

⇒ f' = s x 50

⇒ s = 1 / 50 

∴ s = 0.02

The slip of the motor is 2%.

• Three-phase induction motor is self-starting, because winding displacement is 120 degrees for each phase and supply also has 120 phase shift for 3-phase.
• It results in a unidirectional rotating magnetic field is developed in air gap which causes 3-phase induction motor to self-start.

• The single-phase induction motor is non self-starting in nature.
• When single phase AC supply is given to stator winding of single-phase motor, it produces alternating flux i.e. which alternates along one space axis only.
• It is not synchronously revolving (or rotating) flux, thus it cannot produce any rotation. Hence single phase induction motor is not self-starting.
• To overcome this problem and to make the motor self-starting, it is temporarily converted into two-phase motor during starting.
• For this purpose, the stator of a single phase motor is provided with extra winding known as starting winding in addition to the main winding. These two winding are placed across the single phase supply.

Concept:

For the induction machine, the value of slip is given by

$s=\frac{N_s-N_r}{N_s}$

Where,

N_S is the synchronous speed of the induction machine

N_r is the rotor speed of the induction machine

Application:

In the induction generator operation, a prime mover drives the rotor at speed greater than the synchronous speed. That is, N_r > N_s

Therefore, under such condition, the value of slip s is negative for the induction generator.

Speed control methods of 3 phase induction motor are given by

From the stator side:

• v/f control or frequency control
• changing the number of stator poles
• controlling supply voltage
• adding rheostat in the stator circuit

From the rotor side:

• adding external resistance on the rotor side
• cascade control method
• Injecting slip frequency emf into the rotor side

Almost 90% of the induction motors are squirrel cage type because they have the simplest and most rugged construction.

The differences between the slip ring and squirrel cage induction motor are given below:

Food mixer:

• It is an electric domestic appliance which is used to mix, juice, grind and blend the fruits and food grains.
• The motor housing differs widely depending on the manufacturer. Special care to be taken for vibration-free running.
• Safety features such as overload trip, jar mounting lock (fixing) and proper lid closing are included in the appliances.
• An AC universal motor is housed in the base. The jar contains the cutting knives which is the heart of the blending action
• A food mixer power rating ranges from 100 to 750 watts. The revolution of the food mixer is 3000 to 14000 revolutions per min.
• The desired speed is selected on the control switch. A tapped field coil enables speed selection through a rotary or push button switch. The food mixer normally runs at 3 speeds.
• The time rating of running the mixer varies from 1 minute to 60 minutes depending upon the type.

Universal motor:

• Universal motor is a commutated series-wound motor
• It can operate on either AC or DC power and uses an electromagnet as its stator to create its magnetic field
• These motors are generally series wound (armature and field winding are in series), and hence produce high starting torque
• So, universal motors are generally built into the device they are meant to drive as they have variable speed characteristics.
• Most of the universal motors are designed to operate at higher speeds, exceeding 3500 rpm

The various applications of the universal motor are as follows:

• Portable tools and drill machine
• Used in hair dryers, grinders and table fans
• It is also used in blowers, polishers, vacuum cleaners and kitchen appliances

Slip w.r.t. forward field

$s_f=s=\frac{n_s-n}{n_s}=1-\frac{n}{n_s}$

Since the backward rating flux rotates opposite to the stator, the sign of n must be changed to obtain a backward slip.

$s_b=\frac{n_s-\left(-n\right)}{n_s}=\frac{n_s+n}{n_s}=1+\frac{n}{n_s}$

Adding 

$s_a+s_b=\left(1-\frac{n}{n_s}\right)+\left(1+\frac{n}{n_s}\right)$

$s_b=2-s$

Stepper motor: it is a special type of synchronous motor which is designed to rotate through a specific angle (step) for each electrical pulses received by its control unit. The input command is in the form of a train pulse to turn a shaft through a specified angle.

Advantages:

• Compatible with the digital system
• No sensors are needed for position and speed sensing

Types of stepper motor:

Variable – reluctance stepper motor:

• It consists of single or several stacks of stator and rotor.
• Stator have a common frame and rotor have a common shaft.
• Stator and rotor teeth are of same number and size.
• Rotors are unexcited while stators are pulse excited. The static torque acting on the rotor is a function of angular misalignment θ.
• The rotor locks into stator in position θ = 0° or $\theta =\frac{360}{T}$  where T= no of rotor teeth
• Stator teeth of various stacks differ by angular displacement of $\alpha =\frac{360}{nT}$ where n= no of stacks.
• Directional control is possible with three or more phases.

Permanent magnet stepper motor:

• The rotor is made of ferrite or rare earth material which is permanently magnetised. Rotor move in steps of 22.5°
• This motor operates at larger steps up to 90° and a maximum response rate of 300 pulses per second.

Hybrid stepper motor:

• This is a permanent magnet stepper motor with the toothed and stacked rotor of the variable reluctance motor.
• Compared to permanent magnet motor finer steps for better resolution are obtained in hybrid motor by increasing the number of stack teeth and also by adding additional stack pans on the rotor.
• As compared to variable reluctance motor a hybrid motor requires less stator excitation current because of the PM excited rotor.

• The split-phase motor is also known as a resistance start motor
• It has a single cage rotor, and its stator has two windings known as main winding and starting winding
• Both the windings are displaced 90 degrees in space
• The main winding has very low resistance and a high inductive reactance whereas the starting winding has high resistance and low inductive reactance
• The direction of rotation of a resistance split-phase single-phase induction motor can be reversed by reversing either the auxiliary terminals or the main terminals