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Electrical Machinery [ Electrical Machines ] By Ps Bimbhra Pdf Download

You all know we recently launched free electrical engineering pdf books to all. In this post we are sharing a very good book on electrical machines by ps bimbra , he is a very good author of so many electrical engineering books some of them are mentioned below,
1. Electrical Machinery by ps bimbhra
2. Power electronics by ps bimbhra
3. Generalised theory of electrical machines by ps bimbhra

Electrical Machines PS Bimbhra  PDF Free Download 

User Ratings: *****A Lecturer - Abhishek TiwariI have referred to this for many topics in Electrical Machines. This books gives a detailed explanation of design and working of electrical machines. It a good book to refer for undergraduate students.
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Electrical machinery ps bimbhra will cost us around Rs.400 /- in india. To provide this book for students who can't afford we are sharing  "electrical machinery by ps bimbhra".you can download this pdf directly into your computer or mobile phone easily.You need to have any pdf reader to read this book.

Download Here: Link 1 | Link 2

Note: Due to space on server some times file may get deleted.Please mail us at electricaledition@gmail.com if you face any problem.

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Welding Transformer Working Principle and Applications

Welding Transformer Working Principle and Applications &characteristics of welding transformer

Now a days we have many ac power supplies. So the usage of welding transformer has significant role in welding compared to a motor generator set. When we need to use a motor generator set for welding we need to run it continuously which produces a lot of noise. With the help of welding transformer weld is done with a less noise. Now let us see in detail about welding transformer.

Construction of welding transformer:

1. Welding transformer is a step down transformer.

2. It has a magnetic core with primary winding which is thin and has large number of turns on one arm.

3. A secondary winding with less number of turns and high cross-sectional area on the other arm.

4. Due to this type of windings in primary and secondary it behaves as step down transformer.

5. So we get less voltage and high current from the secondary winding output. This is the construction of ac welding transformer. 

6.A dc welding transformer also has same type of winding the only difference is that we connect a rectifier(which converts ac to dc) at the secondary to get dc output. 

7.We also connect a inductor or filter to smooth the dc current. This will be construction of dc welding transformer. The diagrams are shown below.


Fig 1.DC welding transformer




Fig 2.AC welding transformer

Note:

Many people have a doubt which is primary winding and which is secondary winding. The winding which is connected to power supply is called primary winding and the winding to which load is connected is called secondary winding.

Working of welding transformer:

1.As it is a step down transformer we have less voltage at secondary which is nearly 15 to 45 volts and has high current values which is nearly 200 A to 600 A it can also be higher than this value.

2. For adjusting the voltage on secondary side there are tappings on secondary winding by this we can get required amount of secondary current for welding.

3. These tappings are connected to several high current switches.

4. Now one end of secondary winding is connected to the welding electrode and the other end is connected to the welding pieces as shown in fig 2. 

5.When a high current flows a large amount of  I2R heat is produced due to contact resistance between welding pieces and electrode. 

6.Because of this high heat the tip of electrode melts and fills the gap between the welding pieces.

This is how a welding transformer works.

Volt - ampere characteristics of welding transformer:

Figure given below shows the volt - ampere characteristics of welding transformer.

Arc control of welding transformer:

The impedance of welding transformer must be higher than the normal transformer to control arc and also to control current. 

We can use different reactors for controlling the arc. They are

1.Tapped reactor.

2.Moving coil reactor.

3.Magnetic shunt reactor.

4. Continuously variable reactor.

5. Saturable Reactor.

Now let us see each of this methods for arc control of welding transformer in detail.

1.Tapped reactor:

Below is the circuit for arc control using tapped reactor is given below.

  
With the help of taps we control the current. It has limited current control.

2. Moving coil reactor:

Below is the circuit for arc control using moving coil reactor.





The distance between primary and secondary decides the amount of current. If the distance between the primary and secondary is high then the current is less.

3. Magnetic shunt reactor:

Below is the circuit for arc control using magnetic shunt reactor.
By adjusting the central magnetic shunt flux is changed. By changing the flux current can be changed.

4. Continuously variable reactor:

Below is the circuit for arc control using continuously variable reactor.



By varying the height of reactor core insertion is changed. If core insertion is greater reactance is higher so output current will be less.

5. Saturable reactor:

Below is the circuit for arc control using saturable reactor.

The reactance of the reactor in this is adjusted by changing the value of d.c. excitation which is obtained from d.c. controlled transducer. Higher the d.c. currents, reactor approaches to saturation. This changes the reactance of reactor. By changing the reactance current can be changed.

By using above reactors current can be controlled which helps to control the arc.

In this post we have learnt about welding transformers.

To download this post on welding transformers as PDF click here.

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Operational Amplifier as Integrator and Differentiator/OP Amp Differences between Integrator and Differentiator

Operational amplifier as integrator and differentiator

Operational amplifier which is called also called as op-amp has a key role in many electronic applications due to its special characteristics. Name itself indicates that it can perform operations. By using op-amp we can perform different operations like addition, subtraction, multiplication, differentiation and integration. Of these op-amp application as integrator and differentiator is very common.

                  Before going to see op-amp as integrator and differentiator let us first understand working principle of operational amplifier.

Operational amplifier working principle:

Let us see the symbol of operational amplifier and its terminals before going to see working of op-amp.
It has two input terminals one is marked negative and other as positive and one output terminal. The input terminal which is marked negative is called inverting input because when we apply an input signal to this inverting input we get a phase shift of 180° in the amplified output signal with respect to the applied input signal. The input terminal which is marked positive is called Non-inverting input because when we apply an input signal to this Non-inverting input there is no phase shift between input signal and amplified output signal.

                             It has two input power supply terminals +Vs and -Vs. +Vs is connected to positive terminal of battery and -Vs is connected to negative terminal of other battery. If we require a ground we need to provide ground separately as there is no common ground provided in op-amp.

Open loop operation of op-amp:

In this open loop operation we apply two input signals one at inverting input and other at Non-inverting input as shown in the figure.


 So it has differential input(since one is + and other is -) which means difference of two applied input signals and one output is obtained. The gain of open loop operation of op-amp is given by

Gain = output / input

Aol = Vo / V1 - V2

so output voltage is


Vo is output voltage

V1 is voltage at non-inverting terminal 

V2 is voltage at inverting terminal 

V1 - V2 is differential input voltage

Aol is open loop gain

Open loop gain is very high even a small signal given at input amplifies to large amount but its value will not exceed the supply voltage of op-amp as it obeys law of conservation of energy.

Closed loop operation of op-amp:

If we introduce a feed back in the circuit it is called closed loop operation. Here a part of output signal is fed back to one of the input terminals. The terminal where feed back is given two signals are present simultaneously one is feed back signal and the other is original applied signal it can be seen in the following diagram.
If we apply feed back signal from output to non-inverting terminal it is called positive feed back which is used in oscillator circuits. And if we apply feed back signal from output to inverting terminal it is called negative feedback here phase shift is present between applied signal and feed back signal. This negative feed back is used for amplifier circuits. Closed loop gain of op-amp is given by


Acl = Vo / V1 - V2

 Now output voltage will be


where Vd = V1 - V2.

Acl = closed loop gain.

As we have learnt operation of op-amp now we can clearly understand the application of op-amp as differentiator and integrator.

Op-amp as integrator:

When an operational amplifier work as integrator we get output as integration of voltage with respect to time. Here we use capacitors at a right place in the circuit which helps to perform integration of applied input voltage. The arrangement can be seen from the following diagram.
                           
The above circuit is called an ideal op-amp integrator circuit.

Here the negative feed back is taken and a capacitor is connected between output terminal and inverting input terminal. Because of negative feedback node X is at virtual ground and if the input voltage is 0 V then no current flows through input resistance Rin then the capacitor will remain uncharged. So we get output as 0 V.

                          Now if we apply a constant positive DC voltage at the input then  we get a linearly falling voltage at output. If we apply a constant negative DC voltage at input then we get a linearly raising voltage at output. And this rate of change of output voltage will be directly proportional to input voltage. 

Output voltage calculation:

Now we calculate the output voltage of this circuit.

According to virtual ground concept as non-inverting terminal is grounded then node X will also be at ground potential

                                                            VX = VY = 0
For an ideal op-amp input impedance is high so input current is very less and the current flowing through resistor R1 also flows through capacitor C.

Input current equation is given by,

I = (Vin – VX) / R1 
I = Vin / R1.

output current equation is given by

I = C [d(VX – Vout)/dt] = -Cf[d(Vout)/dt]

Now we equate both current equations as current flowing through resistance R1 (input) and capacitor C (output) are same(since op-amp has high input impedance all current flows through capacitor). We get,

                                         [Vin / R1] = – C [d(Vout)/dt]

Apply integration on both sides, now we get,



The above equation clearly says that output voltage is - 1 / R1 . C times the integration of input voltage. This shows that op-amp acts as an integrator by this circuit arrangement. Here R1.C is called integrator time constant and negative sign shows that there is a phase shift of 180° between input and output voltage. The phase shift is because we have applied signal to inverting terminal.

                        We use integrator circuit to convert a square wave input to triangular wave output as shown in the following circuit.


As discussed when we apply constant positive dc voltage we get a falling output voltage at linear rate and if we apply constant negative dc voltage we get a rising output voltage at linear rate(if a step signal is integrated we get ramp signal).

An integrator op-amp circuit acts as low pass filter it attenuates high frequency signals.

OP-amp as differentiator:

A differential op-amp has output voltage which is proportional to rate of change of input voltage. This op-amp can act as differentiator by keeping a capacitor in series with the input voltage source. This can be seen from the diagram given below 

The capacitor acts as open circuit for dc input. Here we ground the non-inverting terminal of op-amp and the inverting input terminal is connected to output through a feed back resistor Rf. This makes the circuit to behave as voltage follower. The input current to op-amp is very less due to high input impedance of op-amp we have same current through capacitor and resistor Rf.

Output voltage calculation:

Now we calculate the output voltage of this circuit.

According to virtual ground concept as non-inverting terminal is grounded then node X will also be at ground potential

                                                            VX = VY = 0

Input current is given by,

                            I = C [d(Vin-Vx)/dt] = C [d(Vin)/dt]

output current is given by,

                            I = -{(Vout-Vx)/Rf} = -{Vout/Rf}

 Now we equate both equations as current through capacitor and resistor are same.

                            C{d(Vin)/dt} = -Vout/Rf

                            Vout = -C.Rf {d(Vin)/dt 

The above equation clearly says that output voltage is - C.Rf  times the differentiation of input voltage. This shows that op-amp acts as adifferentiator by this circuit arrangement.     Here    Rf.C is called differentiator time constant and negative sign shows that there is a phase shift of 180° between input and output voltage. The phase shift is because we have applied signal to inverting terminal.

                Here if we give a square wave input to differentiator the output has to be zero( since differentiation of constant is zero) but we get negative and positive spikes because input signal takes time to change from 0 to Vm. At constant positive DC input we get negative spike at output and at constant negative DC input we get positive spike at output. This can be seen from the following diagram.

 If we give a sin wave as input to differentiator we get cos wave as output.

                              Vout = -C.Rf {d(Vm sin ωt)/dt}

                               Vout = – Vm. ω. cos ωt consider(C.Rf = 1)

This can be seen in the following diagram


A differential op-amp circuit acts as high pass filter it attenuates low frequency signals.

In this post we have learnt op- amp as integrator and op-amp as differentiator.

To download this post on operational amplifier as integrator and differentiator as PDF clik here


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Conversion from binary code to gray code and gray code to binary code

Conversion from binary code to gray code and gray code to binary code


 In this post let us see conversion from binary code to gray code and gray code to binary code.


Purpose for converting binary code to gray code?

Gray code has occupied a prominent role now-a-days because of its special characteristics. It is, there is change in only one bit for two successive values. This gray code is widely used for error correction in digital communications.

Steps to convert from binary code to gray code:

Let us consider an example to clearly understand the conversion from binary code to gray code

Consider binary code = 1110

Now represent this binary code as b3 b2 b1 b0 = 1 1 1 0

Let the representation of this binary code in gray code be g3 g2 g1 g0

Here b3, g3 are called most significant bits(MSB) and b0,g0 are called least significant bits(LSB).

Step 1: The most significant bit(MSB) of gray code is equal to most significant(MSB) bit of binary code.

In this example g3 = b3 = 1.

Step 2: Now the second most significant bit i.e,which is adjacent to most significant bit(MSB) in the gray code is equal to the sum of most significant bit(MSB) and second most significant bit of binary code. If addition produces any carry ignore the carry.

Note:

Carry is produced when we add two 1's i.e, 1 + 1 = 0, 1 is carry( from Boolean algebra) 

In the following example

g2 = b3 + b2

g2 = 1 + 1 = 0, carry 1 is neglected.

Step 3: The third most significant bit of gray code i.e, which is adjacent to the second most significant bit in the gray code is equal to the sum of second most significant bit and third most significant bit of binary code. If any carry is generated ignore it.

In the considered example:

g1 = b2 +b1

g1 = 1 + 1 = 0, carry 1 is neglected.

Step 4: The above process is continued until the least significant bit(LSB) of gray code is obtained. This least significant bit (LSB) of gray code is obtained by adding last most significant bit and the least significant bit of binary code.If any carry is produced that has to be neglected.

In the following example we have,

g0 = b1 + b0.

g0 = 1 + 0 = 1.

So finally we get the gray code as g3 g2 g1 g0 = 1 0 0 1

Diagrammatically conversion from binary code to gray code  can be represented as follows,

binary code to gray code
Example can be represented diagrammatically as follows,

Conversion from Binary code to Gray Code

 Hence by following above steps conversion from binary code to gray code is done.

Steps to convert from binary code to gray code:


Let us consider an example to clearly understand the conversion from gray code to binary code. 



Consider gray code = 1001.



Now represent this gray code as g3 g2 g1 g0 = 1 0 0 1.

Let the representation of this gray code in binary code be b3 b2 b1 b0.

Here b3, g3 are called most significant bits(MSB) and b0,g0 are called least significant bits(LSB).

Step 1: The most significant bit(MSB) of binary code is equal to most significant(MSB) bit of gray code.

In the example,

b3 = g3 = 1.

Step 2: Now the second most significant bit i.e,which is adjacent to most significant bit(MSB) in the binary code is equal to the sum of most significant bit(MSB) of binary code( It is obtained from step 1) and second most significant bit of gray code. If addition produces any carry ignore the carry.

In this example,

b2 = b3 + g2.

b2 = 1 + 0 = 1.

Step 3: The third most significant bit of binary code i.e, which is adjacent to the second most significant bit in the binary code is equal to the sum of second most significant bit of binary code(It is obtained from step 2)and third most significant bit of gray code. If any carry is generated ignore it.

In the considered example,

b1 = b2 + g1.

b1 = 1 + 0 = 1.

Step 4: The above process is continued until the least significant bit(LSB) of binary code is obtained. This least significant bit (LSB) of binary code is obtained by adding last most significant bit of binary code and the least significant bit of gray code. If any carry is produced that has to be neglected.

In this example,

b0 = b1 + g0.

b0 = 1 + 1 = 0, 1 is carry it is neglected.

So finally we get the binary code as b3 b2 b1 b0 = 1 1 1 0.

Diagrammatically conversion from gray code to binary code can be represented as follows,

Conversion from Gray Code to Binary Code


Example can be represented diagrammatically as follows,

Conversion from Gray Code to Binary Code Example

Hence by following above steps conversion from  gray code to binary code is done.

Today in this post we have learnt conversion from binary code to gray code and gray code to binary code.

This post on conversion from binary code to gray code and gray code to binary code can be downloaded as PDF here.
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Synchronization of alternator and methods of synchronization of alternator

Synchronization of alternator and methods of synchronization of alternator

What is meant by synchronization of alternator?

Connecting a group of alternators parallel to a bus bar and the alternators should have same voltage and frequency as that of bus-bar. This is called synchronization of alternator. There are some conditions to be satisfied by the alternators which are to be connected in parallel to bus-bar to be in synchronization.

Conditions for synchronization of alternators: 

1. The terminal voltage of incoming alternator must be equal to the bus bar voltage.

2. The frequency of voltage generated by incoming alternator must be equal to busbar frequency.

3.The phase sequence of the three phases of the incoming alternator must be same as phase sequence of bus-bars.

4. The phase angle between the voltage generated by incoming alternator and voltage of bus-bar must be zero.

5. Always connect running alternator to bus-bar. If a stationary alternator is connected to bus-bar it will result in short circuit of stator winding.

The above conditions are to be satisfied by alternators to satisfy synchronization.

Why synchronization of alternators is necessary?

1.An alternator cannot deliver power to electric power system until its voltage,frequency,phase sequence and other parameters matches with the network to which the the alternator is connected.

2. The case of synchronization arises because we are connecting many alternators in parallel to supply the demanded load. So we need to match all the parameters of connected alternators with bus-bar to deliver power to load.

3. By synchronization we can match all the parameters of one alternator with the other alternator and also with the bus-bar and deliver the required power to load.

4. Synchronization of alternator is also called as paralleling of alternators.

Advantages of paralleling of alternators: 

We get a common doubt why we need to supply the load by paralleling small units of alternator rather than using a single larger unit? This is because we have many advantages by doing so. They are:

Continuity of service: 

In case of any damage to one of the alternators it can be removed.Supply to load is not interrupted because other alternators can supply the required load. But if u use a larger single unit even a small damage causes the interruption of supply.

Requirement of load:

As the load demanded is not same all the time, during light load periods we can run two or three alternators in parallel. When the demand is high we can add the required amount of alternators in parallel to meet the load demanded.

Reliability:

Several single units connected in parallel is more reliable than single larger unit because if a single unit gets damaged it can be removed and its work is compensated by other units which are running.

High efficiency:

An alternator runs efficiently when it is loaded at their rated value. By using required number of alternators for required demand i.e, light load or peak load we can load an alternator efficiently.

So because of above advantages we use paralleling of alternators.

Steps to connect alternators in parallel or synchronization of alternators:



1.Consider an alternator-1. It is supplying power to bus bar at rated voltage and frequency.

2. Now we need to connect another alternator let it be alternator-2 in parallel with the alternator-1. In order to match the frequency of alternator-2 with the frequency of bus-bar or alternator-1 (since alternator-1 and bus-bar are already in synchronism) we need to adjust the speed of alternator-2. Now the voltage of alternator-2 is to be matched with the voltage of bus-bar or voltage of alternator-1 (since alternator-1 and bus-bar are already in synchronism). For this purpose we need to vary the field rheostat until the voltage matches.

3. The three phase voltages generated by alternator must be same as the three phase voltages of bus-bar or alternator-1(since alternator-1 and bus-bar are already in synchronism).This can be achieved by matching the phase sequence and frequency of alternator-2 with bus bar or alternator-1(since alternator-1 and bus-bar are already in synchronism) phase sequence and frequency.

By following these steps synchronization of alternators is possible.


Methods for synchronization of alternators:

There are three methods for synchronization of alternators. These methods check whether the above mentioned conditions for synchronization of alternators is satisfied or not. The three methods are.

1. Three dark lamps method.

2. Two bright, One dark method.

3. Synchroscope method.

Three dark lamps method for synchronization of alternators:

Let us study synchronization of alternators using three dark lamps method in detail.

Circuit diagram for synchronization of alternators using three lamp method:




Procedure:

1. Consider alternator-1 is supplying power to load at rated voltage and rated frequency which means alternator-1 is already in synchronism with bus-bar.

2. Now we need to connect alternator-2 in parallel with alternator-1.

3. Across the 3 switches of alternator-2 three lamps are connected as shown in the figure.

4. To match the frequency of alternator-2 with the bus-bar frequency we need to run the prime mover of alternator-2 at nearly synchronous speed which is decided by the frequency of bus-bar and number poles present in alternator-2.

5. To match the terminal voltage of alternator-2 with bus-bar voltage we need to adjust the field current of alternator-2 until terminal voltage of alternator-2  matches with the bus-bar voltage. The required value of voltage can be seen in the voltmeter connected to bus-bar.

6.To know whether the phase sequence of alternator -2 matches with the bus-bar phase sequence we have a condition. If all the three bulbs ON and OFF concurrently then we say the phase sequence of alternator-2 matches with the phase sequence of  bus-bar. If the bulbs ON and OFF one after the other then the phase sequence is mismatching.

7. To change the connections of any two leads during the mismatch of phase sequence first off the alternator and change the connections.

8. ON and OFF rate of bulbs depends upon frequency difference of alternator-2 voltage and bus-bar voltage. Rate of flickering of bulbs is reduced when we match the frequency of alternator-2 with bus-bar voltage by adjusting the speed of prime mover of alternator-2

9. If all the conditions required for synchronization are satisfied then the lamps will become dark. 

10. Now close the switches of alternator -2 to synchronize with alternator-1.

11. Now the alternators are in synchronism.

Disadvantage of three dark lamps method for synchronization of alternators:

Flickering only says difference between frequency of voltages of alternator and bus bar but correct value of frequency of voltage of alternator cannot be found.

For example, if the bus bar frequency of voltage is 50 HZ and difference in frequency of voltage of bus-bar and alternator is 1 HZ the alternator frequency of voltage can be either 49 HZ or 51 HZ.

Two bright and one dark lamp method for synchronization of alternators:

Let us discuss synchronization of alternator using two bright and one dark lamp method.

Circuit diagram for synchronization of alternators using two bright and one lamp method:


Procedure:

1. Consider alternator-1 is supplying power to load at rated voltage and rated frequency which means alternator-1 is already in synchronism with bus-bar.

2. Now we need to connect alternator-2 in parallel with alternator-1.

3. Here lamp L-2 is connected similar to the three dark lamp method.

4. Lamps L-1 and and L-3 are connected in different manner. One end of lamp L-1 is connected to one of the phases other that the phase to which lamp L-2 is connected and the other end of lamp L-1 is connected to the phase to which lamp L-3 is connected.

5.Similarly one end of lamp L-3 is connected to a phase other than the phase to which lamp L-2 is connected and other end of lamp L-3 is connected to the phase to which lamp L-1 is connected as shown in the following circuit.

6. To match the terminal voltage of alternator-2 with bus-bar voltage we need to adjust the field current of alternator-2 until terminal voltage of alternator-2  matches with the bus-bar voltage. The required value of voltage can be seen in the voltmeter connected to bus-bar.

7. Depending upon the sequence of lamps L1,L2, L3 becoming dark and bright we can decide whether the alternator-2 frequency of voltage is higher or lower than bus-bar frequency.

8. If the sequence of bright and dark of lamps is L1-L2-L3 then the frequency of voltage of alternator-2 is higher than the bus-bar voltage. Now until the flickering reduces to a low value decreases the speed of prime mover of alternator-2.

9. If the sequence of bright and dark of lamps is L1-L3-L2 then the frequency of voltage of alternator-2 is less than the bus-bar voltage. Now until the flickering reduces to a low value increase the speed of prime mover of alternator-2.

10. When the  L1 and L3 are equally bright and lamp L2 is dark then close the switches.

11. Now the alternators are in synchronism.

Disadvantage of two bright and one dark lamp method for synchronization of alternators:

Phase sequence of the alternator cannot be checked by this method.

Synchroscope method for synchronization of alternators:

Let us discuss synchronization of alternator using synchroscope method.

Circuit diagram for synchronization of alternators using synchroscope method:


Procedure:

1. A synchroscope is used to achieve synchronization accurately.

2. It is similar to two bright and one dark lamp method and tells whether the frequency of incoming alternator is whether higher or lower than bus bar frequency.

3. This contains two terminals they are a) existing terminal b) incoming terminal.

4. Existing terminals are to be connected to bus-bar or existing alternator here in the diagram it is alternator-1 and incoming terminals are connected to incoming alternator which is alternator-2 according to the diagram which we have considered.

5. Synchroscope has a circular dial inside which a pointer is present and it can move both in clockwise and anti clockwise direction.

6. To match the terminal voltage of alternator-2 with bus-bar voltage we need to adjust the field current of alternator-2 until terminal voltage of alternator-2  matches with the bus-bar voltage. The required value of voltage can be seen in the voltmeter connected to bus-bar.

7. Depending upon the rate at which the pointer is rotating the difference of frequency of voltage between incoming alternator and bus-bar can be known.

8. And also if the pointer moves anti clockwise then the incoming alternator is running slower and has frequency less than the bus bar or existing alternator frequency and if the pointer moves clock-wise then the incoming alternator is running faster and has frequency greater than bus-bar or existing alternator frequency. So by adjusting the speed of prime mover of incoming alternator we can match the frequency with bus bar or existing alternator frequency. Frequency matches when the pointer is straight up-wards. At this point close the switch.

9. Now both the alternators are in synchronism.

So by these three methods synchronization of alternators is checked.

Today in this post we have learnt what is meant by synchronization of alternator and methods of synchronization of alternator.

To download this post on synchronization of alternator and methods of synchronization of alternator as PDF click here.
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Electrostatic type instruments working principle, construction, torque equation and extending range

Working principle, construction , torque equation and extending range of electrostatic type instruments 

Hello readers,

                         In this post we are going to discuss about construction principle and torque equation of electrostatic type instruments.


Working principle of electrostatic type instruments:

Working principle of electrostatic type instruments is electrostatic effect.

What is meant by electrostatic induction??

To understand clearly about electrostatic effect see the below circuit.


1.Here the two plates are being charged by a high voltage battery. 

2. Due to this one of the plate gets positive charge and the other plate gets negative charge.

3. Here the deflecting torque is produced by this static electrical field due to attraction present between these opposite charges.

4. The plates move because of the electrostatic force(attraction between plates) that has been produced because of this induced charges.

This effect is called electrostatic effect. 

Construction of electrostatic type instruments:

1. Linear type electrostatic instruments.

2. Rotatory type electrostatic instruments.

Linear type electrostatic instruments:

1. Here one of the plates is fixed and the other plate is movable and these plates are charged as shown in the above circuit. So one of the plate gets positive charge and the other plates gets negative charge. Due to this there will be force of attraction between the plates so the movable plate moves towards the fixed plate until movable plate gains maximum amount of electrostatic energy. Fixing pointer to the movable plate we can measure the voltage. These are called linear type electrostatic instruments.

Rotatory type electrostatic instruments:

2. Here we have a rotatory plate. Due this movement of rotatory plate there may be force of attraction or repulsion between the plates. These are called rotatory type electrostatic instruments.

Torque equation of electrostatic type instruments:

Now let us see torque equation of both linear type electrostatic instruments and rotatory type electrostatic instruments.

Torque equation of linear type electrostatic instruments:

Let us see in detail about torque equation of liner type electrostatic instruments.

Observe the following diagram.


1.Here plate A is fixed and it is positively charged and plate B is movable and it is negatively charged.

2. As the forces are opposite we have attraction between plates. So there will be linear motion between these plates.

3. As there is force between these plates at equilibrium electrostatic force will be equal to spring force.

4.Now electrostatic energy stored in the plate is given by,
                               
                                                                                          
5.Now let us increase the voltage by a small amount let it be dv due to this there will be displacement of plate let the displacement be dx. So work done against the spring force due to displacement of  plate B be F.dx.  Relation between current and applied voltage is given by,

                                                     
6. Now the input energy from this value of electric current is given by,


7. Now the change in this stored energy is given by,

                                                      
8. Now apply principle of energy conservation by neglecting the higher order terms in the expression.

Input energy to the system = increase in the stored energy of the system + mechanical work done by the system.

By substituting all the values we get,

                                     
Now the equation of force from the above equation is given by,

                                       

Torque equation of rotatory type electrostatic instruments:

Let us see in detail about torque equation of rotatory type electrostatic instruments.

Observe the following diagram.


1. By replacing F, dx in equation (1)  by Td , dA respectively we get deflecting torque of rotary type electrostatic instruments.

2. So the deflecting torque is given by,

                                                 
3.At steady state we have controlling torque is given by, Tc = K × A. Where A is the deflection and it is given by,

                                                   

As the deflection is directly proportional to square of voltage we have non- uniform scale.

Hence we have derived  torque equation of  electrostatic type instruments i.e for liner type electrostatic instruments and  rotatory type electrostatic instruments.

Generally electrostatic type instruments are used for measuring high voltages.

The main advantage of using electrostatic type instruments as voltmeters is we can extend the range of voltage that is to be measured.

Methods to extend the range of voltage to be measured for electrostatic instruments:  

1. Resistance potential dividers.

2.Capacitor multiplier technique.

Resistance potential dividers to extend the range of voltage to be measured for electrostatic instruments:  

Now let us see how to extend the range of voltage to be measured by using resistance potential dividers.

To understand it see the below circuit.

Circuit diagram of resistance potential dividers to extend the range of voltage to be measured for electrostatic instruments:  

The following diagram shows the circuit to extend the range of voltage to be measured by 
electrostatic instruments using resistance potential dividers.
                                               

Procedure to extend the range of voltage to be measured by electrostatic instruments using resistance potential dividers:

1. Across r which is total resistance apply the voltage which is to be measured.

2. Across R which is a part of total resistance r connect an electrostatic capacitor.

3.Make one assumption that the capacitor which is connected is having infinite leakage resistance in case if we apply dc voltage. Here the multiplying factor is ratio of resistances i.e, r/R. Multiplying factor in ac case is same as dc case.

Capacitor multiplier technique to extend the range of voltage to be measured for electrostatic instruments: 

Now let us see how to extend the range of voltage to be measured by electrostatic instruments
 using capacitor multiplier technique.

To understand it see the below circuit.

Circuit diagram of capacitor multiplier technique to extend the range of voltage to be measured for electrostatic instruments:  

The following diagram shows the circuit to extend the range of voltage to be measured by electrostatic instruments using capacitor multiplier technique.


capacitor divider

Procedure to extend the range of voltage to be measured by electrostatic instruments  using capacitor multiplier technique:

Let us calculate the multiplying factor.

1. From diagram we have series combination of capacitors. The equivalent capacitance is given by
                                            
2. Voltmeter impedance is given by Z1 = 1/jωC1 . Now total impedance is given by,

                                   
                                                          
3.Multiplying factor is given by,

                                                      Z/Z1 = 1 + C2 / C1.

In this way we can extend the range of voltage to be measured by electrostatic instruments with the help of  resistance potential dividers and capacitor multiplier technique.

Advantages of electrostatic type instruments:

1. As the deflection torque is directly proportional to square of voltage we can measure both a.c and d.c voltages by using electrostatic type instruments.

2.High values of voltage can be measured  using electrostatic type instruments.

3. Current drawn by electrostatic type instruments  is low so power consumption of electrostatic type instruments is low.

Disadvantages of electrostatic type instruments:

1.Electrostatic type instruments have non uniform scale.

2.Electrostatic type instruments are larger in size.

3.Electrostatic type instruments are costlier compared to other type of instruments.

4.Various operating forces present in electrostatic type instruments are small in magnitude.

Today we have learnt working principle, construction , torque equation and extending range of electrostatic type instruments.

You can download this article about working principle, construction , torque equation and extending range of electrostatic type instruments as PDF here.                     
                                                                                 
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Speed Control Methods Of DC Motor

Speed Control Methods Of DC Motor

DC motors brought us revolutionary changes in industrial and domestic applications.This all because of an unique feature of DC motors i.e, speed controlling of DC motors .Compared to Synchronous motor , Induction Motor controlling the speed of DC series or DC shunt motor is very easy and efficient. Now let's get into the detailed explanation on how we can control speed of DC motor ?

What is speed control?

Speed controlling is nothing but changing our DC motor speed according to our requirements.We have different methods to control speed.DC motors are majorly categorized into DC series motors and DC shunt motors. We have separate methods of speed control for dc series motors and dc shunt motors.

Factors on which speed control of dc motors lie: 

In DC motor an EMF induced in armature conductors due to the rotation of armature in magnetic field this is called back EMF (Eb). The magnitude of the Eb can be given by the EMF equation of a DC generator.

Eb = PØNZ/60A

(where, P = no. of poles, Ø = flux/pole, N = speed in rpm, Z = no. ofarmature conductors, A = parallel paths)

Ecan also be given as,
Eb = V- IaRa
thus, from the above equations
N = Eb 60A/
but, for a DC motor A, P and Z are constants
Therefore, N  K Eb/Ø          (where, K=constant)

This shows the speed of a dc motor is directly proportional to the back emf and inversely proportional to the flux per pole.

Speed control methods of dc motor:

As said above we have separate speed control methods for both dc shunt motors and dc series motors.

Let see each of them in detail.

Speed control of dc shunt motor:

There are three methods by which speed control of dc shunt motor is done.
1.Flux Control Method.
2.Armature Control Method.
3.Voltage Control Method
Voltage control method is further divided into two:
a) Multiple voltage control.
b) Ward-Leonard System.


Speed control of dc shunt motor by flux control method:

As we said speed of dc motor is inversely proportional to flux per pole. So by decreasing the flux per pole the speed of the dc shunt motor can be increased. To decrease the flux per pole we need to add a rheostat in series with the shunt field winding as shown in the following circuit.
                                    
By increasing the resistance current If decreases so flux decreases. As flux decreases speed of dc shunt motor increases as speed is inversely proportional to flux. This method is efficient because If2Rf value is small because If is small. It has limitation though it can gain maximum speed. Limitation arises because weakening of flux beyond the limit will adversely affect the commutation.

Speed control of dc shunt motor by armature control method:

As discussed speed of a dc motor is directly proportional to back e.m.f  Eb where Eb = V - IaRa. By keeping V and Ra constant back e.m.f  Eb depends on Ia.Add a resistance in series to the dc shunt motor armature as shown in the following circut.


Now by increasing the resistance current decreases.As current decreases back e.m.f  Eb decreases. As back e.mf Eb decreases speed of the dc shunt motor decreases.

Speed control of dc shunt motor by voltage control method:

1. Multiple voltage control:

In this method the armature is supplied with variable voltage with the help of a suitable switch gear.The voltage across the shunt field is maintained constant. As the speed of dc shunt motor is directly proportional to voltage across the armature the speed of dc shunt motor can be controlled accordingly.  

2. Ward - leonard system:

To understand speed control of dc shunt motor by this method see the circuit diagram given below.
Here motor M1 drives the generator G. Motor M1 has constant speed. M2 is the motor whose speed is required to be controlled.Generator G is coupled to M2.Here the voltage from the generator G is supplied to armature of motor M2. The voltage supplied by the generator can be varied smoothly with the help of field regulator . So by Ward - leonard system smooth speed control of dc shunt motor is obtained.

Speed control of dc series motor:

There are three methods for controlling speed of dc series motor.

1. Flux Control Method
This is further divided into four types. They are 
a) Field divertor.
b)Armature divertor.
c)Tapped field control.
d)Paralleling field coils.
2. Armature - resistance control.
3. Series - parallel control.

Speed control of dc series motor by flux control:

Let us discuss speed control of dc series motors by different flux control methods.

Speed control of dc series motor by flux control by using field divertor:

Here we connect a variable resistance in parallel with the series field of dc series motor as shown in the following circuit.

As we have connected a variable resistance in parallel with the series field some of the current that has to flow through series field is diverted to variable resistance( this is the reason why it is called divertor). So the current flowing through the series field decreases as current decreases flux decreases. We know speed of dc motor is inversely proportional to flux as flux decreases speed of dc series motor increases so we can achieve high speeds with this method of speed control of dc motor.

Speed control of dc series motor by flux control by using armature divertor:

In this method we connect a variable resistance parallel to armature of dc series motor as shown in the following circuit.

 As we have connected variable resistance in parallel to armature the armature current Ia decreases.We know torque equation for a dc series motor is Ta ∝ ØIa. So for a constant load torque if Ia decreases flux Ø increases to maintain load torque constant. So the dc series motor draws more current from the supply so flux Ø increases as flux increases speed decreases as speed of dc motor is inversely proportional to flux. In this way the speed of dc series motor can be achieved by this method.

Speed control of dc series motor by flux control using tapped field control:

Here the series field winding has tapping as shown in the following circuit.
By selecting the suitable tap the number of turns connected in the circuit can be changed. We know speed of dc motor is inversely proportional to flux by changing the number of turns of series field connected in circuit the flux can be changed. If more number of are turns are connected to the circuit then current decreases so flux decreases. As flux decreases speed increases. If number of turns connected in the circuit are less current will be high. As current is high flux will be high so speed of dc series motor will be less. So according to the required speed we can choose the required number of turns and control speed of dc series motor.

Speed control of dc series motor by flux control using paralleling field coils: 

Here the series field coils are regrouped and are connected in parallel as shown in the following circuit diagram.
As the series field winding is regrouped and connected in parallel the flux will decrease since current decreases.As speed of dc motor is inversely proportional to flux the speed of dc series motor will be high. According to the required speed i.e, high or less the coils are regrouped.

Speed control of dc series motor by armature - resistance control:

In this method we connect a variable resistance in series with the series field winding as shown in the following circuit.
By adding the resistance in series with the series field the voltage across the armature is reduced. As the speed of dc series motor is directly proportional to voltage across the armature the speed of dc series motor is reduced accordingly. This is the most common method for speed control of dc series motor.

Speed control of dc series motor by series - parallel control:

This method is generally applicable for electrical traction. For two or more dc series motors which are coupled this method is possible. In this method to gain less speeds the two series motors are connected in series. In series current is high(as current division is not there) we get high current as current is high flux is high. As speed of dc motor is inversely proportional to flux we get low speed. When the two dc series motors are connected in parallel the current is less( since current s divided between two series motors)as current is less flux is less so high speed is obtained. So according to the required speed we connect the dc series motors either in series or parallel. The circuit diagram for speed control of dc series motor by this method is shown below.
In this way speed control of dc series motor and dc shunt motor can be done.

In this post we have learnt speed control of dc motors. To download this post on speed control of dc motors as PDF click here.
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