Induced EMF Per Phase in Synchronous Machines: A Detailed Mathematical Approach
Induced EMF Per Phase in Synchronous Machines: A Detailed Mathematical Approach Introduction Electromotive force (EMF) is a fundamental concept in electrical machines, particularly in synchronous machines. The induced EMF per phase plays a crucial role in determining machine performance. This article provides a detailed mathematical derivation of the induced EMF equation for a synchronous machine. Fundamental Principles In a synchronous machine, the rotor carries the field winding, which produces a rotating magnetic field when excited by a DC source. The stator contains the armature windings where the EMF is induced due to the relative motion between the stator and rotor magnetic fields. The magnitude of the induced EMF depends on the machine’s design and operating parameters. Derivation of Induced EMF per Phase The induced EMF in a synchronous machine follows Faraday’s Law of Electromagnetic Induction, which states that: E = − N d Φ d t E = -N \frac{d\Phi}{dt} where: E...