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Electrical Machines -1.Electrical Machines -1.
Typology: Lecture notes
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Syllabus:
circuit - comparison with two winding transformers. Poly-phase transformers – Poly-phase connections - Y/Y, Y/Δ, Δ/Y, Δ/Δ and open Δ TEXT BOOKS:
REFERENCE BOOKS:
COURSE OUTCOMES: At the end of this course the student would get
Unit 1: D C Generators
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UNIT – I D.C GENERATORS
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Let l be the length and b be the breadth of the rectangular coil in meters.
According to Faradays law the emf induced in a conductor is given by e =
− N.dØ/dt where e is the induced emf , N is the number of conductors , Ø is the
flux linkage and t is the time. The flux linkage Ø is given by : Ø = B.area of the
coil.cos ωt = B.l.b.Cos ωt
Since we are considering only one conductor the induced emf in the conductor is
given by:
e = - dØ/dt = -d(B.l.b.Cos ωt)/dt = B.l.b.ω .Sin ωt = Em Sin ωt where Em =
B.l.b.ω
As can be seen from the above equation for induced emf the voltage in a given
generator can be increased by either increasing the flux density ‘B’ or the
rotational speed ’ω’.
The induced emf ‘ e’ at any position of the coil as a function of time ‘ t’ as derived
above is then given by : e = Em Sin ωt where Em = B.l.b.ω. As can be seen
dØ/dt i.e rate of change of flux linkage is minimum (=0) when the coil is at
perpendicular position to the flux lines and hence the induced voltage e is also
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minimum (=0). We will call this as position Ѳ = 0^0 at the instant of say t = 0 sec.
And dØ/dt is maximum when the coil is at parallel position to the flux lines and
hence the induced voltage e is also maximum( = Em = B.l.b.ω ) and this position
will then be Ѳ = 90^0 .When Ѳ = 180^0 the induced emf is again zero and when Ѳ =
2700 the emf induced is again maximum but now it would be negative. When Ѳ =
3600 the coil is back to the original position and the induced emf is again equal to
zero. For the two pole generator shown in the figure one complete cycle of
change takes place in one rotation of the coil. A plot of the induced emf ‘e’ as
function of coil position Ѳ is an alternating voltage as shown in the figure below.
Fig: emf induced in a single turn generator in one full revolution
When the two terminals of the coil are connected to an external load (resistance
in this case) through two separate rings (called slip rings) mounted on the
armature current flows through the resistance and the current also would be
sinusoidal.
Action of commutator : We have seen that the output from a simple single turn
generator in one full revolution is a sinusoidal in nature (AC). Commutator is the
most important part of a DC Generator which converts the AC to DC. The current
flowing through the external load can be made unidirectional by replacing the
two slip rings with two split rings as shown in the figure below which is the basis
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In each half revolution the positions of the conductors AB & CD and the segments
P &Q reverse but the brushes B 1 &B 2 are stationary and continue to collect current
from the Positive side and deliver current to the Negative side respectively. Hence
the voltage across the load will be a unipolar voltage as shown in the waveform
above. The changeover of brushes B 1 &B 2 between segments P &Q takes place
when the voltage is minimum so as to avoid or minimize the arcing between the
split segments. In practical generators there will be more number of conductors
and also more number of Pole pairs and hence more number of split segments
are required and such a set of more number of split segments is called
commutator.
Constructional features of a DC Generator:
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Fig: A simplified diagram of a dc machine:
Major parts of a DC generator:
Main frame or Yoke Poles Armature Commutator Brushes ,bearings and shaft
The physical structure of the machine consists of two parts: the stator and the rotor. The stationary part consists of the main frame (yoke), and the pole pieces, which project inward and provide a path for the magnetic flux. The ends of the pole pieces that are near the rotor spread out over the rotor surface to distribute its flux evenly over the rotor surface. These ends are called the pole shoes. The exposed surface of a pole shoe is called a pole face, and the distance between the pole face and the rotor is the air gap. There are two principal windings on a dc machine:
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Stator pole-face. The stator pole shoes, therefore, should be laminated to reduce the eddy-current loss. However, for mechanical reasons, in many cases the whole of the pole core is laminated. In DC Machines of high ratings slots are cut on the pole-faces to house a separate winding called the compensating winding. The compensating winding is connected in series with the armature winding and neutralises the effect of armature reaction. To neutralize the effect of armature reaction in the space in between two poles, smaller poles, called interpoles, are fixed on the yoke as shown in Fig. 2.2.
Figure: Cross sectional view of a DC Machine showing Interpoles
As mentioned earlier, the armature winding is placed inside the armature slots. The slots are lined with tough insulating material. This slot insulation is folded over the armature conductors. The conductors in the slots are secured in their places by hard wooden wedges or fiber glass wedges. The armature windings are first made on formers and then placed on slots. Enamel insulated copper wires are used for the armature winding. Each armature coil end is connected with each segment of the commutator.
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A commutator is a cylindrical body mounted on the shaft along with the armature. In fact, the armature core and the commutator form one single unit mounted on the shaft. Brushes are placed on the commutator surface to supply or collect current to the armature coils through the commutator segments. The commutator segments are insulated from each other. The function of the commutator is to convert alternating currents induced in the armature conductors into direct currents in the external circuit in case of a DC Generator operation. In the case of a dc motor the function of the commutator is to produce a unidirectional torque. The commutator is of cylindrical structure and is built up of a wedge-shaped segment of hard-drawn copper. Mica insulation is provided between commutator segments. Brushes are made of carbon and are housed in brush-holders. A spring in the brush-holder maintains the desirable pressure on the carbon brushes so that proper contact is maintained between the brushes and the commutator surface.
The armature windings are vital part of a DC Machine. This is where emf is induced in the case of a Generator and and force is developed that results in the turning of the rotor in the case of a Motor. The design of the armature winding is more critical than the design of other parts of a DC machine. The armature winding is housed in slots made on the armature surface. Formed coils are placed on slots. The ends of the coils are joined with commutator segments. Commutator: The commutator is made up of a number of commutator segments. Coil-ends are connected to each commutator segment. The segments of the commutator are made of hard-drawn copper and are separated by thin sheets of mica or micanite ( insulator). The induced emf per conductor in a DC machine is small. The problem is how these conductors are to be connected together so as to form a complete winding. Figure below shows the cross-sectional view of the armature of a four-pole machine.
For ease of understanding, a developed diagram of armature of Fig. (a) below is drawn as shown in Fig. (b). Conductors should be so connected that the total emf
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The average pitch Ya , back pitch Yb , and the front pitch Yf are calculated as: Ya = 16/4= 4 Ya = ( Yb + Yf ) / Yb – Yf = ± For progressive lap winding Yb – Yf = 2 Yb = 5 , Yf = 3
Figure gives the details of end connections of the conductors, connection of coils with commutator segments, and the position of brushes on the commutatorsurface with their polarities. This type of winding is called lap winding. In the winding shown in Fig. 2.11, single-turn conductors are used. As many as 16 conductors make eight coils. The coils are 1-6, 3-8, 5-10, 7-12, 9-14, 11-16, 13-2 and 15-4. The design of a lap winding of the type shown in Fig. 2.11 is described as follows. 2.3.2 Lap Winding In a lap winding, the finishing end of one coil is connected via the commutator segment to the starting end of the adjacent coil situated under the same pole. In this way all the coils are connected. The winding is known as lap winding because the sides of successive coils overlap each other (see Fig. below). A coil may consist of any number of turns. The number of slots required on the armature is equal to the number of coil sides if two coil-sides are placed in each slot. With two coil- sides in each slot, a two layer winding is obtained. While making a winding diagram in a two-layer winding, all top coil-sides are numbered odd whereas the bottom coil-sides are numbered even (shown by dotted lines) as shown in Fig.. For an eight-coil armature, therefore, eight slots are required on the armature surface. The following terminologies are required to be understood for preparing an armature winding diagram.
Pole Pitch: It is equal to the number of coil-sides per pole. For a single turn, eight coil, four-pole armature pole pitch is calculated as:
Pole pitch ( Ya ) = (No. of coils x 2)/ No. of poles = (8 x 2) /4 = 4
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Figure: Position of coil-sides in slots of a two-layer armature winding
Coils and Coil-sides: The DC armature windings are double-layer type having at least two coil-sides per slot. Each coil consists of an upper coil-side at the top of one slot and a lower coil-side situated at the bottom of another slot. The distance between the two coil-sides of a coil is approximately equal to the pole pitch. A coil may be of single turn or of many turns. If two coil-sides are placed in one slot, then the number of slots required on the armature for housing the coils is equal to the number of coils of the winding. For low-speed high-voltage winding, however, the number of coil-sides per slot is more than two. This is because the winding will have a large number of coils and it may not be possible to have an equal number of slots on the armature. Back Pitch : The distance measured in terms of the number of armature conductors (coil sides) between the two coil-sides of a coil measured around the back of the armature, i.e., away from the commutator end of the armature is called the back pitch, Yb.
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(iv) The commutator pitch is equal to m, i.e., equal to 1, 2, etc. for simplex, duplex etc. type of winding. (v) The number of parallel paths in the armature winding for a simplex lap winding is equal to the number of poles, P. (vi) The resultant pitch is always even, being the difference of two odd numbers.
Example 1 : Prepare a layout winding diagram for a simplex lap-type DC armature winding. The winding is for 4 poles. The armature has 16 slots and 16 commutator segments. Solution: Number of armature coils = Number of commutator segments = 16 Number of coil-sides (conductors) Z = 16 × 2 = 32 Back pitch Yb =(Z/P) ±1 = (32/4) ±1 = 9 or 7 Yb – Yf = 2 Yf = Yb – 2 = 9 – 2 (using Yb = 9) = 7 Yb = 9 Yf = 7 Since Yb > Yf , the winding is a progressive one. As there are 32 coil-sides and 16 slots, the number of coil-sides per slot is 2. The connection scheme of the coil-sides is shown in Figure. below
Figure: Scheme for connections of the coil-sides of a DC armature windings
Coil-side 1 is connected to coil-side 10 on the other side of the commutator (since Yb is 9, coil-side 1 is connected to coil-side 1 + 9, i.e., 10). Coil-side 10 is connected
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to coil-side 3 on the commutator end (Since Yf is 7, coil-side 10 is connected to coilside10–7, i.e., 3). The winding progresses according to the above scheme. It may be noted that each coil is used once and the winding is a closed one. The layout diagram of the winding along with commutator connections and brush positions is shown below.
Connections of the coil-sides are made as follows: for connections at the back end of the armature, add the back pitch with the coil-side which is to be connected. Thus coil-side 1 is to be connected with coil-side 1 + Yb, i.e., 1 + 9 = 10. On the commutator end side, coil-side 10 is connected to coil-side 3. This is achieved by subtracting Yf , i.e., 7 from coil-side number 10 (10 – 7 = 3). Coil-side 3 is now connected to 3 + Yb = 3 + 9 = 12. In this way the winding is completed. The positions of the four poles are also shown in Fig. 2.15. Eight coil-sides placed in four slots are under each pole. Assuming a direction of rotation of the armature, say anticlockwise in Fig. 2.15, the direction of the induced emf in the armature conductors is determined by applying Fleming’s right-hand rule. The direction of the current in the coil-sides under north poles will be downward and under south poles upward as shown in Fig. 2.15. The position of brushes can be determined by tracing the directions of current in various coil-sides. From Fig. 2.15, it can be observed that directions of current in coil-sides 1 and 8 are downward and they are connected to commutator segment
