Showing posts with label DC Machines. Show all posts
Showing posts with label DC Machines. Show all posts

## Condition for Maximum Efficiency of DC Machine

We have discussed about construction & working of DC machine. In this article  condition for maximum efficiency in DC machine will be derived.

### Condition for Maximum Efficiency in DC Machine

In this DC generator is taken as reference to find out maximum efficiency .The DC generator efficiency is perpetual but varies with load. Think through a shunt generator supplying a load current IL at a terminal voltage V.

Then Generator output  =  VIL
Generator input  =  Output + Losses

=  VI+ Variable losses + Constant losses
=  VI+ I2R+ Wc
=  VIL + (IL + Ish2)Ra + Wc  ( ∵  Ia = IL + Ish)

The shunt field current Ish is generally small as compared to Iand, therefore, can be neglected.
Generator input   =  VIL + I2a Ra + Wc

### Now                Efficiency   η  =  output / Input

=  VI/ (VIL + I2a Ra + Wc
=  1 / {1+[(ILRa/V)+(Wc/VIL)]}
The efficiency is always maximum when the denominator of above equation  is minimum i.e.,
d/dI{( ILRa/V) + (Wc+VI2L)} =0
Or
(Ra/V) – (Wc/ VI2L) =0
Or
Ra/V = Wc/VI2L
Or
I2LRa = Wc

I.e. Variable loss = Constant loss (IL ≈ Ia)
The load current corresponding to maximum efficiency is given by;

I= √ Wc/Ra

Therefore, the efficiency of a DC generator will be maximum when the variable loss is equal to the constant loss.

## Losses In DC Generator (DC Machines)

In the previous articles we discussed about DC generator working, Voltage equation of dc generator. Efficiency is a very important specification of any type of electrical machine. When we talk about efficiency, losses comes into the picture. DC generator efficiency can be calculated by finding the total losses in it. There are various losses in DC generator. We classified DC generator losses into 3 types.

### Total Loss in a D.C. Generator

(a)  Copper Losses
(b)  Magnetic Losses
(c)   Mechanical Losses
The above 3 losses are primary losses in any type of electrical machine except in transformer. In transformer there are no rotating parts so no mechanical losses.
Let us have a brief discussion on each and every loss in dc generator.
(a)  Copper Losses
Copper losses occur in dc generator when current passes through conductors of armature and field. Due the resistive property of conductors some amount of power wasted in the form of heat. Most of the time we neglect copper losses of dc generator filed, because the amount of current through the field is too low [Copper losses=I²R, I² will be negligible if I is too small].
Note : EgIa is the power output from armature.
If we consider all losses,
Total Copper Losses=I²Ra
Where Ra = resistance of armature and interpoles and series field winding etc.
(i) Field copper loss. In the case of shunt generators, it is practically constant and Ish² Rsh (or VIsh). In the case of series generator, it is = Ise²Rse where Rse is resistance of the series field winding. This loss is about 20 to 30% of F.L. losses.
(ii) The loss due to brush contact resistance. It is usually included in the armature copper loss.
Armature copper loss = I2a Ra

Shunt field copper loss = I2shRsh

Series field copper loss = I2se Rse

Note: There’s additionally brush contact loss attributable to brush contact resistance (i.e., resistance in the middle of the surface of brush and commutator). This loss is mostly enclosed in armature copper loss.
(b)  Magnetic Losses (also known as iron or core losses),
Hysteresis losses or Magnetic losses occur due to demagnetization of armature core. This losses are constant unless until frequency changes. Eddy current losses are due to circular currents in the armature core.
We know armature core is also a conductor, when magnetic flux cuts it, EMF will induce in the core, due to its closed path currents will flow. This currents causes eddy current losses.
(i) hysteresis loss, Wh B1.6 max f and
(ii) eddy current loss, We  max f ²
These losses are practically constant for shunt and compound-wound generators, because in their case, field current is approximately constant.
Both these losses total up to about 20 to 30% of F.L. losses.

(c) Mechanical Losses.
We know generator is a rotating machine it consist of friction loss at bearings and commutator and air-friction or windage loss of rotating armature. We can’t neglect this losses because they always present , These are about 10 to 20% of F.L. Losses.
The total losses in a d.c. generator are summarized below :
Stray Losses
Usually, magnetic and mechanical losses are collectively known as Stray Losses. These are also known as rotational losses for obvious reasons.

Total loss = armature copper loss + Wc = Ia²Ra + Wc = (I + IshRa + Wc.
Armature Cu loss Ia²Ra is known as variable loss because it varies with the load current.
Total loss = variable loss + constant losses Wc

## Poor commutation | Sparking in DC Machines

### Sparking in DC Machines at Brushes

Poor commutation and sparking are caused by distortion of main field flux. The sparking at the brushes results in poor commutation due to inability of the current in the short circuited coil to reverse completely by the end of short circuit period (Usually of the order of 1/500). The main reason to delay this quick reversal is due to the production of self induced e.m.f in the coil undergoing commutation. This self induced e.m.f in the coil undergoing commutation is known as reactance voltage which is of Small magnitude and produces a large current through the coil whose resistance is less due to short circuit. If this voltage exceeds more than 30 or 40 V, a  spark spreads around the commutator in the form of ring fire.

Sparking results in overheating at the commutator. This poor commutation may be caused by mechanical or electrical condition. The mechanical conditions are uneven commutator surface, non-uniform brush pressure vibration of brushes in the holder. The electrical conditions include an increase in the voltage between the commutator segments an increase in the current density at the trailing edge of the brush etc.

#### Minimization of Sparking in DC Machines

By using interpoles we can improve the commutation i.e., making the current in the short circuited coil to attain its full value in the reverse direction by the end of short circuit period.

Interpoles or compoles are small poles fixed to the yoke and are placed in between the main poles. These poles are connected in series with the armature, so that they carry full armature current. Their polarity is same as that of the main pole. They induce an e.m.f. in the coil under commutation known as commutating e.m.f or reversing e.m.f (reversal of current).

This reversing emf neutralizes the reactance emf thereby making commutation spark less.

## Types of D.C Machines [DC Generators & DC Motors]

### Types of D.C Machines [DC Generators & DC Motors]

A DC machine is an electromechanical energy conversion device. It requires magnetic flux conductors and the relative motion for the energy conversion. Based on the production of magnetic flux (i.e., exciting the field winding) the DC machines are classified as follows.

1.Permanent Magnet Type D.C Machines

This type of machines are of low rating and consists of the magnetic poles fixed in the inner periphery and the armature coils feed or being fed by the supply in case of generator and motor respectively.

2.Electromagnet Type D.C Machines

A) Separately Excited DC Generator

In the separately excited machine the field windings are being fed by a separate D.C source (battery) and the. e.m.f generated in case of generator would be the sum of the supply voltage and the armature resistance drop.

B) Self Excited DC Generator

In case of self excited machines, the field winding is connected to the armature, so that the armature could feed the field coils. Let us consider, these conditions of connecting field winding in case of generators.

a) Shunt Wound DC Generators

If the field winding is connected across the armature winding then the machine is called the shunt machine. In the shunt generator, as the shunt winding has to overcome the generated voltage it has to be made with higher turns of lower cross-sectional conductors. They have higher resistance as compared to the series coils,but the current is less.
Let,
Rsh = Shunt winding resistance
Ish = Current flowing through the shunt field
Ra = Armature resistance
Ia = Armature current
V = Terminal voltage
Eg = Generated emf

Ia=Ish + IL

Shunt field current, Ish = V/Rsh

Voltage across the load,  V = Eg-Ia Ra
Power generated, Pg= Eg×Ia
Power delivered to the load, PL = V×IL

b) Series Wound DC Generators

In this type of generator the field coils are connected in series with the armature terminals and the conductors would be of higher cross- section and with lesser number of turns.

The current flowing through the coil would be the same as that of the armature current. So, it is made with higher cross-sections.

From above connections,
Ia = Isc = IL=I (say)
Voltage across the load, V = Eg -I(Ia×Ra)
Power generated, Pg = Eg×I
Power delivered to the load, PL = V×I

c) Compound Generator

The combination of two windings i.e., series winding and shunt field winding is considered as a compound generator. In the compound generator, normally the field of the shunt will be more'than the series field and will be less than the individual shunt machine. The same is the case with the series field also.

Based on the type of connection of the shunt field to the armature and series field it is classified as,

(i) Long shunt, (ii) Short shunt.

(i) Long Shunt Compound Wound DC Generator

In this type of compound machine, the series current and the armature current is made , same and the shunt connection is made after the series connection is done.

Series field current = Armature current

Shunt field current, Ish=V/Rsh
Armature current, Ia= series field current, Isc= IL+Ish
Voltage across the load,  V=Eg-Ia Ra-Isc Rsc=Eg-Ia (Ra+Rsc) [∴Ia=Ics]
Power generated, Pg= Eg×Ia
Power delivered to the load, PL=V×IL

(ii) Short Shunt Compound Wound DC Generator

In this type of machine, the series field current is made same to that of the line current. The connection of shunt field is done first and then to the series field.

Series field current, Isc = IL
Shunt field current, Ish = (V+Isc Rsc)/Rsh
Armature current, Ia = Ish + IL
Voltage across the load,  V = Eg - Ia Ra - Isc Rsc
Power generated, Pg = Eg×Ia
Power delivered to the load, PL=V×IL

Whatever the connection of machine long or short shunt machines, if the flux produced by the series field aids with the shunt field then the machine is called cumulative compound machine or if the series field opposes the shunt field then the machine is called the differential compound machine.

## Commutation In DC Machine [Generator or Motor]

### Commutation Definition

This is post about commutation in dc generator and dc motor. The reversal of current in the armature winding by means of commutator bar and brushes is known as commutation process.

Necessity of Commutation In DC Machine

Commutation serves two purposes,
1. It converts alternating current to direct current
2 It maintains rotor magnetomotive force stationary in space.

### Concept of Commutation in DC Machine

Commutation process in DC machine can be explained  by assuming commutator bar width is equal to brush width and insulation between the commutator bar is of negligible thickness.

For understanding the physical concept behind the process of communication, let us consider, five instants of commutator working with respect to brushes. The armature of the considered D.C, machine is rotating from left to right.

At the first instant, the brush is completely situated on commutator bar A and it is delivering 2Ic (current) current Ic flows through coil A from left to right as shown in below figure .

At the second instant, when the brush comes in contact' with bar 2, coil A gets short circuited. If the current from bar B to brush is I2 then current in coil A changes from 2Ic to (Ic — I2). In order to produce output current from brush as 2Ic the commutator bar delivers 2Ic — I2 current to the brush as shown in below figure.

At the third instant, when the brush occupies the equal area of bar A and bar B, now coil A carries no current, bar A and bar B delivers the same amount of current Ic to the brush as shown in below figure.

At the fourth instant, when the armature and commutator bar rotation increases, the brush occupies the large area of bar B. Area of contact between brush and bar decreases thus decreasing the current in bar A to ie.,During this instant, coil A carries current Ic - I1 from right to left. Here, bar B carries (2Ic-I1) current so that brush delivers the output current of 2Ic as shown in the below figure.

At the fifth instant, when brush occupies the complete area of bar B, now the coil A is open circuited and therefore carries current from right to left as shown in below figure.

Commutation Period (Tc)

It is defined as the time taken by coil A to change current Ic from +Ic to -Ic.
Mathematically commutation commutation period (Tc) may be defined as,

### Commutation in D.C. Generator

As D.C. generator consist of two brushes and they are placed on opposite sides of commutator each brush slides along one half of commutator and then follows the other half forming a loop.

During the instant when loop reaches the point of rotation the voltage induced reverses the polarity, the brush shifts from one commutator segment of other therefore indicating that one brush is positive with respect to others. The voltage between the brushes fluctuates in amplitude between ‘0’ and maximum value.

### Commutation in D.C. Motor

The process of commutation in DC. motor is same as DC. generator but the only difference is the power is transferred from terminal to the armature by means of brushes and commutator.

### Causes of Poor Commutation

Poor commutation is caused due to,
1. Poor mechanical conditions like uneven surface of commutators, vibrations of brushes etc.
2. Poor electrical conditions such as increased voltage between the bars of commutators, increase in the current density of brushes etc.

## Compensating Windings and Interpoles in DC Generator

### Compensating Winding and Interpoles in DC Generator

In DC compound machine setup by armature current opposes magnetic field flux, this is known as armature reaction. The armature reaction has two effects (i) Demagnetizing effect and (ii) Cross magnetizing effect. Demagnetizing effect weakens the main field flux which in turn decreases the induced e.m.f (as E  Ø)). To overcome this effect a few extra turns/poles are added in series to main field winding. This creates a series field which serves two purposes,

(i) It helps to neutralize the demagnetizing effect of armature reaction.

(ii) If wound for cumulative compounded machine the electrical performance will be improved.

### Compensating Winding

All armature conductors placed under the main poles region produces e.m.f which is at right angle (90°) to the main field e.m.f. This e.m.f causes distortion in main field flux. This is known as cross magnetizing effect. To minimize the cross magnetizing effect compensating winding is used. This compensating winding produces an m.m.f which opposes the m.m.f produced by armature conductors.

This objective. is achieved by connecting compensating winding in series with armature winding. In absence of compensating winding, cross magnetizing effect causes sparking at the commutators and short circuiting the whole armature winding.

Let, Zc = Number of compensating conductors/pole
Za = Number of active armature conductors/pole
Ia = Armature current.
ZcIa= Za (Ia/A)
Where,
Ia/A=Armature current/conductor

Zc= Za/A

This winding neutralizes the cross magnetizing effect due to armature conductors only but not due to interpolar region. This winding is used in large machine in which load is fluctuating.

### Interpoles

Cross magnetizing effect in interpolar region is by interpoles (also known as compoles (or) commutating poles). These interpoles are small in size and placed in between the main poles of yoke. Like compensating winding, interpoles are also connected in series with armature winding such that the m.m.f produced by them opposes the m.m.f produced by armature conductor in interpolar region. In generators, the interpole polarity is same as that of main pole ahead such that they induce an e.m.f which is known as commutating or reversing e.m.f. This commutating e.m.f minimizes the reactance e.m.f and hence sparks or arcs are eliminated.

Compensating winding and interpoles are used for same purpose but the difference between them is, interpoles produce e.m.f for neutralizing reactance e.m.f whereas compensating winding produces an m.m.f which opposes the m.m.f produced by conductors.

## Armature Reaction In DC Machines

### Armature Reaction In DC Machines [Motor & Generator]

What is Armature Reaction?

The effect of magnetic field set up by the armature current on the distribution of flux under the main poles of a DC generator or a DC motor is known as armature reaction.

The armature m.m.f produces two undesirable effects on the main field flux. They are,
1. Distortion of the main field flux wave along the air gap periphery.
2. Net reduction in the main field flux per pole.

Reduction in main field flux per pole reduces the generated voltage and torque, whereas distortion of main field flux gives three harmful effects. They are increase in iron losses, poor commutation and sparking.

Consider a two-pole machine as shown in figure [in graph] at no-load i.e., having no armature currents. The main field flux is shown on a horizontal phasor OA which is produced by field m.m.f (IfNf).

MNA (Magnetic Neutral Axis) :

MNA (Magnetic Neutral Axis) may be defined as the axis along which no emf is generated in the armature conductors as they move parallel to the flux lines. Brushes are always placed along MNA because reversal of current in the armature conductors takes place along this axis.MNP refers to magnetic neutral point which is a point on MNA

GNA (Geometrical Neutral Axis):

GNA (Geometrical Neutral Axis) may be defined as the axis which is perpendicular to the stator field axis.GNP refers to geometrical neutral point which is a point on GNA

The geometrical neutral plane and the magnetic neutral plane are coincident at no-load, i.e., magnetic lines of force intersect the MNA at right angles.

If D.C machine is loaded then the armature winding receives the current. These currents are shown in figure by dots under south pole and by crosses under north pole. These currents setup armature flux. Armature flux (φa)is shown by a vertical phasor OB.φa is produced by armature m.m.f IaNa. If the D.C machine is working as generator, then its armature must be driven clockwise by prime mover and anti-clockwise for motoring operation.

From above figure  it is seen that φa is perpendicular to φf i.e., the path of armature flux crosses the path of main field flux.This effect is known as cross magnetizing effect.

If the current is flowing in both the windings, the resultant flux distribution is obtained by super imposing the two fluxes as shown in below figure.

From above, it is clear that armature flux aids the main field flux at upper end of north pole and at lower end of south pole. The DC machine practically gets saturated and the strengthening effect is very low as compared with weakening effect and the resultant flux get decreased from its no-load value.

This effect on armature flux is called demagnetizing effect. This effect reduces the total flux/pole and found to be 1 to 5% from Its no-load to full—load.

#### How To Reduce Armature Reaction?

Usually, no methods employed for small machines (up to few kilowatts) to reduce the armature reaction. But for large DC machines, interpoles and compensating winding are used to reduce armature reaction.

### Methods to Reduce Armature Reaction

(a) High Reluctance Pole Tips

By flattening the pole faces slightly so that the air gap is longer at the pole tips rather than at the center of the pole results in increase in reluctance of the pole tips and the magnitude of armature cross flux is reduced and the distortion of the resultant flux density wave is minimized. This can be achieved by using chamfered or eccentric pole face.

(b) Reduction in Armature Flux

To reduce armature cross flux without reducing the a main field flux, it is required to create more reluctance in the path of armature flux. This is done by using field pole laminations.
The reluctance offered to armature flux is more pronounced due to four air gap openings introduced in the path of cross flux.

(c) Strong Main Field Flux

During the design of DC machine, it should be ensured that main field m.m.f should be strong when compared to full load armature m.m.f. The distortion produced by armature cross flux can be minimized by increasing the ratio of main field m.m.f to the full load armature m.m.f.

(d) Interpoles

Interpoles are small poles placed in between the main poles. These are connected in series with armature,so that they carry armature current. The e.m.f induced by the interpoles neutralizes the effect of armature m.m.f in the intelpolar region,. thus making commutation sparkless.

(e) By Using Compensating Winding

A compensating winding is an auxiliary winding embedded in slots located in the faces of main poles. This winding is connected in series with armature in such a manner so that the direction of current flowing in this winding should be quite opposite to the direction of current flowing in the armature conductor the m.m.f produced by the compensating winding should be equal to the m.m.f produced by the armature conductors. To maintain a uniform distribution of flux in the main poles and to neutralize the effect of armature reaction. compensating windings are provided. This winding adds cost of the machine and doubles the armature copper loss. but it makes the machine to withstand the most violent fluctuations of load that is applied to it.