DC GeneratorArmature Windings

Losses&

Efficiency

Conductor:

Every individual length of wire lying in a magnetic field & in which emf is induced.

Turn:

When the two conductors which are lying in the magnetic field are connected in series so that emf which is induced in them help each other or the resultant emf induced becomes double of that due to one conductor.

Coil:

The two wires or conductors AB & CD along with their end connections termed as coil.

Multi turn coil

Single turn coil

The group of conductors or wires constituting a coil side of a multi-turn coil is wrapped with a tape as a unit & is placed in the armature slot. These coils are used when total number of armature conductors are excessive & is not feasible to use single turn coils due to the reason that it will require large number of commutatotor segments.

Pole Pitch:

It is defined asi. The distance between two adjacent polesii. It is equal to the number of armature

conductors (slots) per pole.

Coil Pitch:

It is the distance , measured in terms of armature slots, between two sides of the coil.

Full pitched winding:

Coil pitch or coil span = Pole pitch

Fractional pitched winding:

Coil pitch or coil span > Pole pitch

Full pitched winding

Fractional - pitched winding

Winding pitch: it is defined as the distance between the start of two consecutive coils & is denoted by Y. It has two parts i. Front pitch YF: It is defined as the distance between the second

conductor of one coil & the first conductor of the next coil which are connected together at front .

ii. Back pitch YB : t is defined as the distance, measured in terms of the

armature conductors, which a coil advances on the back of the armature. It is basically the width or span of the coil.

Resultant pitch YR : It is defined as the distance between the beginning

of one coil & beginning of the next coil to which it is connected.

Commutator pitch YC : It is defined as the distance between the segments

to which the two ends of a coil are connected.

Single-layer winding: In this winding one conductor is placed in each armature slot.

Two-layer winding: In this winding two conductors per slot are arranged in two layers. Usually, one side of every coil lies in the upper half of one slot and other side lies in the lower half of some other slot at a distance of approximately one pitch away. Some times 4 or 6 or 8 coil sides are

used in each slot in several layers. The coil sides laying at upper half are

numbered odd. While, at lower half are numbered even.

Multiplex Winding:In such windings, there are several sets of completely closed and independent windings. If there is only one set of closed winding, it is called simplex winding. If there are two such windings on the same armature, it is called duplex winding and so on. The multiplicity affects a number of parallel paths in the armature. For a given number of armature slots and coils, as the multiplicity increases, the number of parallel paths in the armature increases thereby increasing the current rating but decreasing the voltage rating.

il

Simplex Lap Winding: In this type of winding the end of one coil is connected to the beginning of the next coil with the two ends of each coil coming out at adjacent commutator segments. For a progressive lap winding the commutator pitch Yc =1. A typical coil of Nc turns for a simplex lap winding is shown in Figure 1. In the simplex lap winding the number of parallel paths between brushes is equal to the number of poles. This type of winding is used for low-voltage, high-current

Let us consider a four-pole, two-layer, simplex lap winding with 8 slots, as shown. If number of turns per coil Nc=1 , the total number of conductors is Z=2(1)(8)=16. The coil pitch is therefore, Y = 8/4=2 slots

winding connection where the two ends of a coil are connected to adjacent commutator segments. The coils in each path are connected in series and the winding close upon itself.

winding connection where the two ends of a coil are connected to adjacent commutator segments. The coils in each path are connected in series and the winding close upon itself.

The number of parallel path between the brushes and the winding arrangement can be seen more clearly by the developed diagram of the armature

The number of parallel path between the brushes and the winding arrangement can be seen more clearly by the developed diagram of the armature

Simplex wave winding: As we have seen in the lap winding, the two ends of a coil are connected to adjacent commutator segments. In the wave winding, the two ends of a coil are connected to the commutator segments that are approximately 360 electrical degrees apart (i.e., 2-pole pitch). This way all the coils carrying current in the same direction are connected in series. Therefore, there are only two parallel paths between the brushes, i.e., 1Yc = 2a = independent of the number of poles. This type of winding is used for low-current, high-voltage applications

Let there be a 6-pole machine whose armature winding has 648 conductors. Let the average emf induced in each conductor is 2 V and let each conductor be of such a cross section that normal current is 50 A.

When machine is Lap Wound:

Total No. of conductors, Z = 648 Total No. of parallel paths, a = 6Therefore, conductors per parallel paths = 648/6 = 108 emf per parallel path = 108 X 2 = 216 VTotal current = 50 X 6 = 300 ATherefore, output of the generator = 216 X 300 = 64,800 W = 64.8 kW

216 V

300A

50A

50A

50A

50A

50A

50A

50A

648 V

100A

50A

When machine is Wave Wound:

Total No. of conductors, Z = 648 Total No. of parallel paths, a = 2Therefore, conductors per parallel paths = 648/2 = 324 emf per parallel path = 324 X 2 = 648 VTotal current = 50 X 2 = 100 ATherefore, output of the generator = 648 X 100 = 64,800 W = 64.8 kW

It can be thus concluded that whether the winding is lap or wave connected, as far as the output in kW is concerned, that remains the same but output voltage and current are definitely affected.

The lap winding gives greater current at lower voltage while wave winding gives lower current at high voltage.

EMF Equation

Let Φ be the total magnetic flux in webers per pole, Z is the total number of conductors in the slots, and P is the number of poles.

Then, flux cut by one conductor in one revolution = Φ P

The flux cut by one conductor in N rpm = Φ P N The flux cut by one conductor in N rps = Φ P N / 60

Therefore, average emf generated in one conductor = Flux cut per second = Φ P N / 60

The number of conductors in series between positive brush & negative brush = Z / No. of parallel paths through winding = Z / A

Therefore, the total emf generated between terminals = E = (Φ P N / 60) X (Z / A)

Types of Generators

Simple relations:

Armature current Ia = IL Amps

Terminal Voltage V = E – Ia Ra volts

Power developed P = E Ia

Power delivered to load = EIa – Ia

2 Ra = Ia (E – Ia Ra) = V Ia

= V IL

Separately Excited Generator

Simple relations:

Ia = Isc = IL

V = E – I (Ra + RSc)

Power developed P = E Ia

Power delivered to load

= E Ia – Ia2

(Ra + RSc)

= Ia [E – Ia (Ra + RSc)]

= V Ia = V IL

Series Wound Generator

Shunt Wound Generator

Simple relations:

Shunt field current Ish = V/Rsh

Armature current Ia = Ish + IL Amps

Terminal Voltage V = E – Ia Ra volts

Power developed P = E Ia

Power delivered to load

= V IL

Compound Wound GeneratorsShort Shunt Long Shunt

Simple relations: Series current Ise = I a = Ish + IL Amps Shunt current Ish = V / Rsh

Terminal Voltage V = E – Ia(Ra + Rse) volts Power developed, P = E Ia

Power delivered to load PL = V IL

Simple relations: Series current Ise = IL Amps Shunt current Ish = (V + Ise Rse) / Rsh

Terminal Voltage V = E – IaRa – Ise Rse volts Power developed, P = E Ia

Power delivered to load PL = V IL

Losses in a DC Generator

Copper losses

Stray losses

Armature Cu losses

Shunt Cu losses

Series Cu losses

Mechanical losses

Iron losses

Hysteresis

Eddy current

Friction

Windage

Constant Losses

Constant Losses

Power stages in a DC generator

A B C

Iron & Friction Losses = A – BCopper Losses = B – CEfficiency = C / A = V I / BHP X 746

Example:Calculate the emf generated by a 4-pole wave wound armature having 45 slots with 18 conductors per slot driven at 1200 rpm. The flux per pole is 0.016 wb.

Solution:

Given: P = 4, A = 2 {in wave winding A = 2], Z = 45 X 18 = 810 Conductors Φ = 0.016 wb, and N = 1200 rpm.

Now, E = Φ P N Z / 60 A = 0.016 x 4 X 1200 X 810 / 60 X 2 = 518.4 V

Example: A shunt generator delivers 450 A at 230 V and the resistance of the shunt field and armature are 50 ohms and 0.03 ohms respectively. Calculate the generated emf.

Solution:Shunt field current = Ish = V/Rsh = 230 / 50 = 4.6 A Armature current Ia = Ish + IL = 450 + 4.6 = 454.6 A

Terminal Voltage V = E – Ia Ra volts Or, E = V + Ia Ra = 230 + 454.6 X 0.03 = 243.6 V

Q# 1. What emf will be generated in an 8-pole, lap wound generator if it is rotated at 200 rpm. The flux per pole is 0.05 wb and the number of armature conductors is 960.

Q# 2. Calculate the emf generated by a 4-pole wave-wound armature having 45 slots with 18 conductors per slot when driven at 1200 rpm. The flux per pole is 0.016 wb.

Q# 3. A 2-pole generator with a wave-wound armature has 51 slots, each having 24 conductors. The flux per pole is 0.01 wb. At what speed the armature be driven to give an induced emf of 220 volts?

Q# 4. A 30 kW, 300 V, DC shunt generator has armature and field resistances of 0.05 ohms and 100 ohms respectively. Calculate the total power developed by the armature when it delivers full load output.