Electrical Machines · Synchronous Machines

Equation of Induced EMF in Alternators

Dr. Mithun Mondal BITS Pilani, Hyderabad Campus Electrical Machines

Demonstrative Video

SECTION 01

Equation of Induced EMF

\[\begin{array}{cl} Z= & \mbox{No. of conductors}=2T=2\times \mbox{No. of turns per phase}\\ P= & \mbox{No. of poles}\\ f= & \mbox{frequency in Hz}\\ \Phi= & \mbox{flux/pole in webers}\\ K_{d}= & \mbox{distribution factor}=\dfrac{\sin\left(m\beta/2\right)}{m\sin\left(\beta/2\right)}\\ K_{p}= & \mbox{pitch factor}=\cos\left(\alpha/2\right)\\ N= & \mbox{rotor rpm} \end{array}\]
In one revolution of the rotor (i
  • In one revolution of the rotor (i.e. 60/N second) each stator conductor is cut by a flux of \(\Phi P\)

  • \[\begin{aligned} d\Phi & =\Phi P\\ dt & =60/N \end{aligned}\]
    Then,
  • \[\begin{aligned} & =\dfrac{d\Phi}{dt}\\ &=\dfrac{\Phi PN}{60}\\ & =\dfrac{\Phi P}{60}\times\dfrac{120f}{P}\\ & =2f\Phi \end{aligned}\]
    Avg. emf induced per conductor
  • \[=2f\Phi Z=4f\Phi T\]
    For Z-conductors in series/phase, Avg. emf/phase
Equation is for full-pitched and concentrated coils
  • \[=1.11\times4f\Phi T =4.44f\Phi T\]
    R.M.S value of emf/phase
  • Equation is for full-pitched and concentrated coils.

  • \[= \boxed{4.44K_pK_df\Phi T}\]
    Actually available voltage/phase
Key Concepts
  • \[\boxed{K_p = \cos \left(n\alpha/2\right)}\]
    \(K_p = \cos \left(5\alpha/2\right)\)\(5^{th}\)degrees (electrical) for the fundamental flux wave, then for different harmonics If the short-pitch angle or chording angle is
  • \[\boxed{K_{d}=\dfrac{\sin \left(n \cdot m\beta/2\right)}{m\sin \left(n\beta/2\right)}}\]
    Similarly, distribution factor for different harmonics
  • \[\boxed{f_n=nf}\]
    Frequency is also changed.