Electrical Machine 1
Electrical Machines I
Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao
2
Basic Principles
As mentioned earlier the transformer is a static device working on the principle of
Faraday’s law of induction. Faraday’s law states that a voltage appears across the terminals of an electric coil when the flux linkages associated with the same changes. This emf is proportional to the rate of change of flux linkages. Putting mathematically, e= dψ dt (1)
Where, e is the induced emf in volt and ψ is the flux linkages in Weber turn. Fig. 1 shows a
Figure 1: Flux linkages of a coil
coil of N turns. All these N turns link flux lines of φ Weber resulting in the Nφ flux linkages. In such a case, ψ = Nφ and e=N dφ dt volt (3) (2)
The change in the flux linkage can be brought about in a variety of ways • coil may be static and unmoving but the flux linking the same may change with time. 3
Indian Institute of Technology Madras
Electrical Machines I
Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao
• flux lines may be constant and not changing in time but the coil may move in space linking different value of flux with time. • both 1 and 2 above may take place. The flux lines may change in time with coil moving in space. These three cases are now elaborated in sequence below, with the help of a coil with a simple geometry.
L B
X
-
+
Figure 2: Static coil
Fig. 2 shows a region of length L m, of uniform flux density B Tesla, the flux lines being normal to the plane of the paper. A loop of one turn links part of this flux. The flux φ linked by the turn is L ∗ B ∗ X Weber. Here X is the length of overlap in meters as shown in the figure. If now B does not change with time and the loop is unmoving then no emf is induced in the coil as the flux linkages do not change. Such a condition does not yield any useful machine. On the other hand if the value of B varies with time a voltage is induced in the coil linking
Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao
2
Basic Principles
As mentioned earlier the transformer is a static device working on the principle of
Faraday’s law of induction. Faraday’s law states that a voltage appears across the terminals of an electric coil when the flux linkages associated with the same changes. This emf is proportional to the rate of change of flux linkages. Putting mathematically, e= dψ dt (1)
Where, e is the induced emf in volt and ψ is the flux linkages in Weber turn. Fig. 1 shows a
Figure 1: Flux linkages of a coil
coil of N turns. All these N turns link flux lines of φ Weber resulting in the Nφ flux linkages. In such a case, ψ = Nφ and e=N dφ dt volt (3) (2)
The change in the flux linkage can be brought about in a variety of ways • coil may be static and unmoving but the flux linking the same may change with time. 3
Indian Institute of Technology Madras
Electrical Machines I
Prof. Krishna Vasudevan, Prof. G. Sridhara Rao, Prof. P. Sasidhara Rao
• flux lines may be constant and not changing in time but the coil may move in space linking different value of flux with time. • both 1 and 2 above may take place. The flux lines may change in time with coil moving in space. These three cases are now elaborated in sequence below, with the help of a coil with a simple geometry.
L B
X
-
+
Figure 2: Static coil
Fig. 2 shows a region of length L m, of uniform flux density B Tesla, the flux lines being normal to the plane of the paper. A loop of one turn links part of this flux. The flux φ linked by the turn is L ∗ B ∗ X Weber. Here X is the length of overlap in meters as shown in the figure. If now B does not change with time and the loop is unmoving then no emf is induced in the coil as the flux linkages do not change. Such a condition does not yield any useful machine. On the other hand if the value of B varies with time a voltage is induced in the coil linking