Electromechnical Energy Conversion

Electromechnical Energy Conversion are essential to understand. For more visit here.

Every electrical machine makes use of magnetic field energy as an intermediate form of energy in the process of electrical-mechanical energy conversion. i.e energy conversion takes place from electrical energy energy to magnetic field energy to mechanical energy (in case of motor) or vice versa (in case of generator).

Electrical Energy ——>Magnetic Energy——>Mechanical Energy

Mechanical Energy—–>Magnetic Energy——>Electrical Energy

Energy Stored in a magnetic Field – Electromechnical Energy Conversion

Flux density(B) = Flux(Ø)/Area(A)

Flux change of the coil(Ψ) = N X flux(F) (N = number of turns)

 Ψ= NØ                                               Ø = Magnetic flux

Ψ = N(BA)                                           since Ø = BA

H X l = N X i(t)                                    (Ampere’s law)

l = length of magnetic flux

A = corss sectional area of flux path

The instantaneous electrical power input p(t) = e(t)i(t)

Therefore Electrical energy Input during a time δt,

δW = p(t)δt

δW = e(t)i(t)δt

Also e(t) = Ri(t) + dΨ /dt

R = Resistance of the coil

dΨ /dt = rate of change of flux linkage(induced emf)

Electrical energy input in time dt = e.i.dt

                                                          = (Ri + dΨ /dt).i.dt

                                                          = Ri^2.dt + i.dΨ

We know that Ri2.dt is the energy loss in the resistor due to joules heat.Therefore i.dΨ should be equalto magnetic energy stored in the circuit during the period ‘dt’.

(Electrical Energy input) = (Increase in magnetic field energy) + (Energy Loss) + (Mechanical workdone)

Ri2.dt + i.dΨ = dWf +Ri2.dt+ 0

i.dΨ               = dWf            (dWf = stored magnetic field energy)

Therefore total energy stored in the magnetic field = ∫ i.dΨ

But N.i = H.l

            =B.l/μ  = (B.A/μA).l

       N.i = S.Ø                                               (S = reluctance (l/μ.A)

Therefore Wf = ∫S.Ø dØ                         (stored energy in magnetic field)

                  Wf = S.ز/2

Alternative Forms

 Wf = ∫ N.i.dØ                         (stored energy in magnetic field)

       Wf = ∫ H.l.d(BA)                     

        Wf = (l.A) μ.H2/2

Therefore stored energy per unit volume = μ.H2/2 = B.H/2

Wf = ∫ i.dΨ                        (stored energy in magnetic field)

       Wf = ∫ i.d(Li)    =    L∫ i.d(i)              

        Wf = L. i2/2                 (by the definitions self inductance L = Ψ/i )

Electromechnical Energy Conversion details are above

Electromechnical Energy Conversion are essential to understand. For more visit here.