Question 11.3: Show that fast changes are dictated by the effect of leakage...
Show that fast changes are dictated by the effect of leakage in ductances.
In the machine to be investigated, assume that Ls=Lr=2.5, Lm=2.4, and Lsσ=Lrσ=0.1. These are typicalper-unit values for an induction machine. Now Equation (11.56) may be reduced as follows.
\Delta _{\Psi s}=\frac{L_{s}L_{r}L_{m}^{2}}{L_{r}}\Delta i_{s} (11.56)
ΔΨ_{s} = \frac { L_{s} L_{r} – L^{2}_{m} } { L_{r} } Δi_{s} = \frac { (L_{m} + L_{sσ} )(L_{m} + L_{rσ} ) – L^{2}_{m} }{ L_{r} } Δi_{s} = \frac { L^{2}_{m} + L_{m} L_{sσ} + L_{m} L_{rσ} + L_{sσ} L_{rσ} – L^{2}_{m} }{L_{r} } Δi_{s} = \frac { L_{m} L_{sσ} + L_{m} L_{rσ} + L_{sσ} L_{rσ} }{L_{r} } Δi_{s} ≈ \frac { L_{m} ( L_{sσ} + L_{rσ} ) } { L_{r} } Δ i_{s} ≈ (L_{sσ} + L_{rσ} ) Δ i_{s}ΔΨs≈(Lsσ+ Lrσ)Δis = 0.2Δis, while the more accurate value is ΔΨs=0.196Δis, and correspondingly, ΔΨm ≈ LrσΔis = 0.1 Δis while the more accurate value is ΔΨm=0.096Δis. A rapid change in stator current, therefore, passes chiefly through leakage inductances.
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