ee172-chap-1-1-mod.ppt

ELECTRICAL MACHINES EE 172 Presented by: Dr. Francis Boafo Effah  Summary of Course Outline Basic Laws of Electrical Machines D.C. Machines Transformers Induction Machines  CHAPTER 1 BASIC LAWS OF ELECTRICAL MACHINES Faraday’s law of electromagnetic induct...

ELECTRICAL MACHINES EE 172 Presented by: Dr. Francis Boafo Effah  Summary of Course Outline Basic Laws of Electrical Machines D.C. Machines Transformers Induction Machines  CHAPTER 1 BASIC LAWS OF ELECTRICAL MACHINES Faraday’s law of electromagnetic induction Two laws form the basis of operation of electrical machines which are used  to convert electrical energy to mechanical energy or  to convert mechanical energy to electrical energy. The laws are  the Faraday’s law of electromagnetic induction known simply as the law of induction and  the law of interaction. Let  N = the number of turns of electric circuit or coil and  Φ = the total flux linking the circuit or coil. The product λ=NΦ is termed the flux linkage. If the flux linkage is made to change with time an emf is induced in the electric circuit. The instantaneous emf according to Faraday’s law is given by: Example 1 A variable flux  (t ) 0.002 sin 120t links a coil of 4000 turns. Calculate the instantaneous voltage induced in the coil. Solution d d e    4000 0.002 sin 120t  dt dt 960 cos120t Example 2 A coil of 2000 turns surrounds a flux of 5 mWb produced by a permanent magnet. The magnet is suddenly drawn away causing the flux inside the coil to drop to 2 mWb in 1/10 of a second. What is the average voltage induced? Solution  2  1 2  5  3 mWb  3 E N 2000  60 V t 1000 101 Change of flux linkage in coil can occur in two ways:  The flux varies in magnitude with time (As in Example 1). Magnetic fields in engineering devices are mostly produced by electric currents. When the current changes, the field also changes.  There is a relative motion of the coil and the flux (As in Example 2). Mathematically, we can express the flux linkage as a function of position θ and time t and state the Faraday’s law in this form:  d  er . ep  where  dt and t The voltage er, which depends on the speed of the motion is called motional or rotational emf. This voltage, when induced in a machine winding, gives rise to mechanical/electrical power conversion. The voltage ep is called pulsational or transformer emf. It provides a means of electrical energy transfer between magnetically coupled windings as from primary to secondary windings in a transformer. Force on current–carrying conductor A conductor of active length l metres and carrying a current i amps and lying in and perpendicular to the direction of a magnetic field B webers/m2, experiences a mechanical force of magnitude: The force expression given by the above equation is also referred to as the law of interaction. The direction of the force can be determined by applying Fleming’s left hand rule. Example 3 A conductor 3 m long carrying a current of 200 A is placed in a magnetic field whose density is 0.5 Wb/ m2. Calculate the force on the conductor if it is perpendicular to the field. Solution: Voltage induced in a conductor moving in a magnetic field The emf in a single conductor of active length l metres which cuts across a magnetic field of density B webers per m2 when moving at speed u m/s in a direction at right angles to the direction of the flux is given by e Blu volts The equation is referred to as the flux cutting rule. This voltage is the result of the relative motion of conductor and a magnetic field. It is a motional emf. Itsdirection can be determined by applying Fleming’s right hand rule In rotating electrical machines, the change of flux linkage is not clearly defined and it is therefore not easy to calculate the induced voltage using the coils and their flux linkage. The induced voltage is more conveniently calculated using the flux cutting rule which refers to the conductors rather than the coils themselves. Example 4 The conductors of a large generator of length 2 m are moved at right angles across a magnetic field at a constant speed of 100 m/s. The flux density in the magnetic field is 0.6 Wb/ m2. Calculate the emf induced in each conductor. Solution: