I agree that a self-excited (by capacitors) induction generator at no-load as suggested by Gunnar is a better framework for viewing the system.
There is discussion of that in the Induction Motor Handbook and the Variable Speed Generator Handbbok (both by Ian Boldea) – the solution of voltage for a variable speed generator at constant speed (similar to coasting down slowly) and no-load is given by considering a simple circuit of residual voltage source, capacitance and inductance. The tricky part is that the inductance changes with voltage. The net effect imo is that the resonance range is in fact extended beyond what we would see for simple linear system.
Attached is an excerpt from the above text which outlines the analysis to determine operating point (voltage) for induction generator at no-load (I added the red annotations)
As shown on the left side of the figure, there are two branches both connected in parallel to E1 = terminal voltage. One branch is the capacitor, the other is series combination of Erem (residual magnetism) and the magnetizing inductance (which changes)
On the right side the two curves are plotted on a plot of E1 vs I and the operating point will be the intersection.
The capacitor branch is a straight line with slope |Zc| = |1/wC|.
The inductor branch has an offset voltage of Erem, and the slope is the value of Xm at that particular voltage.
In this particular set of parameters plotted, the slopes are the same when the current is near zero... would indicate a resonant condition for the system linearized about that low-excitation point. The voltage increases until the Lm goes into saturation at the operating point.
The slopes are also the same in the middle of the curve, would indicate a resonance at that linearized point as well.
We can certainly see that if we took this system and increased the margin to overexcitation by increasing Xc, we would rotate that Xc line counterclockwise and reduce the voltage. That qualitative feature of the linear/resonant model remains intact.
But it is fundamentally a non-linear system and talking about resonance doesn't really tell the whole picture. There are in fact a wide range of parameters that will lead the system to saturation.
It is not too far from what I said originally – the non-linearity of the system extends the range of resonance. But I do think I was wrong to say that we had to be overcorrected (based on calculations using no-load current at rated voltage/frequency) in order to generate these high voltages near saturation. It is not too hard to imagine that nameplate votlage/frequency condition might correspond to a point toward the right of the curve where the slope of the magnetizing branch (Xm) is less than the slope of the capacitive branch (Xc), i.e. inductive vars more than capacitive vars (undercorrected), and yet the system would still go to the saturated operating point at the far right of the curve.
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