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1 Name two methods that can be used to minimise the effect of hunting in a synchronous motor. 5.2 Define distribution factor. 5.3 Calculate the terminal EMF on open circuit.

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Here are the solutions to Question 5.

Part 5.1

Name two methods that can be used to minimise the effect of hunting in a synchronous motor.

  • Using damper windings (or amortisseur windings) in the rotor pole faces.
  • Using a flywheel to increase the moment of inertia of the rotor.

Part 5.2

Define the term distribution factor.

The distribution factor (kdk_d) is a factor that accounts for the reduction in the induced electromotive force (EMF) in an alternator winding due to the coils being distributed in several slots per pole per phase, rather than being concentrated in a single slot. It is always less than or equal to one.

Part 5.3· 5 steps

Calculate the terminal EMF on open circuit.

Given:

  • Number of poles P=4P = 4
  • Frequency f=50 Hzf = 50 \text{ Hz}
  • Number of phases m=3m = 3
  • Number of slots S=38S = 38
  • Conductors per slot Zs=18Z_s = 18
  • Flux per pole Φ=0.04 Wb\Phi = 0.04 \text{ Wb}
  • Winding type: Single-layer
  • Connection: Mesh-connected (Delta)

  1. Calculate the number of slots per pole (SpS_p) and slots per pole per phase (qq).

    Sp=SP=384=9.5S_p = \frac{S}{P} = \frac{38}{4} = 9.5 q=Spm=9.53=3.1667q = \frac{S_p}{m} = \frac{9.5}{3} = 3.1667

  2. Calculate the electrical angle per slot (β\beta).

    β=360∘S×P2=360∘38×42=360∘38×2=18.947∘\beta = \frac{360^\circ}{S} \times \frac{P}{2} = \frac{360^\circ}{38} \times \frac{4}{2} = \frac{360^\circ}{38} \times 2 = 18.947^\circ

  3. Calculate the distribution factor (kdk_d).

    kd=sin⁡(qβ2)qsin⁡(β2)k_d = \frac{\sin\left(\frac{q\beta}{2}\right)}{q\sin\left(\frac{\beta}{2}\right)} kd=sin⁡(3.1667×18.947∘2)3.1667sin⁡(18.947∘2)k_d = \frac{\sin\left(\frac{3.1667 \times 18.947^\circ}{2}\right)}{3.1667 \sin\left(\frac{18.947^\circ}{2}\right)} kd=sin⁡(30∘)3.1667sin⁡(9.4735∘)k_d = \frac{\sin(30^\circ)}{3.1667 \sin(9.4735^\circ)} kd=0.53.1667×0.16458=0.50.5209=0.9598k_d = \frac{0.5}{3.1667 \times 0.16458} = \frac{0.5}{0.5209} = 0.9598

  4. Calculate the number of turns per phase (NphN_{ph}).

    Total conductors Ztotal=S×Zs=38×18=684Z_{total} = S \times Z_s = 38 \times 18 = 684.
    Conductors per phase Zph=Ztotalm=6843=228Z_{ph} = \frac{Z_{total}}{m} = \frac{684}{3} = 228.
    For a single-layer winding, Nph=Zph2=2282=114 turnsN_{ph} = \frac{Z_{ph}}{2} = \frac{228}{2} = 114 \text{ turns}.

  5. Calculate the EMF per phase (EphE_{ph}).

    Assuming a full-pitch winding, the pitch factor kp=1k_p = 1.
    The formula for induced EMF per phase is Eph=4.44kpkdfΦNphE_{ph} = 4.44 k_p k_d f \Phi N_{ph}.

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