As generators go yours is pretty good on no load and even on load with normal loads it is still better than most. The wriggles are due to slot ripple and would not affect any load.
Driving any non linear load from a small alternator will always mess up the wave form. Single phase makes it far worse with a battery charger.
Your alternator has impedance, when you take current the volts drop, this is inevitable. With a linear load the waveform is not much affected as the volt drop is proportional to the current. The waveform just gets smaller.
With these type of loads the alternator's regulating system corrects the drop in voltage so when you switch on the load you would see a dip for several ac cycles and then the machine volts would recover. When you remove the load it will overshoot a few cycles at higher voltage and again recover.
A battery charger looks more like no load during the centre of the waveform and a large load at the peak, so the peak of the waveform is reduced in relation to the rest.Complicated regulated battery chargers will have somewhat different effects from a simple diode /transformer charger but the problem is similar.
The final waveform is complicated by how the alternator regulating scheme corrects for the drop in voltage. No scheme can correct until the drop takes place, so there must be a step drop in the voltage wave when conduction occurs.
I can't offer you much help in solving the problem, I personally would use a charger separate from the power alternator, driven by its own or the same engine. That doesn't help your problem.
If you can sort out the voltage calibration on the scope, I would look at the peak ac voltage to make sure it is not exceeding the sine wave nominal ( 1.4 x 120 for you probably). If it is peaks that are going high you may be able to limit them with Mov clippers, but they will only manage short fast peaks which you will only see on the scope as very fast low brightness edges. Your waveform is not that bad and it may just be spikes that is causing the trouble.
There is probably little you can do to have much effect on the main alternator waveform. If you are careful a capacitor across the ac line may provide enough initial energy store to carry the current spike for long enough for the alternators regulating system to pick up its field. Be careful, these alternators are not designed to accept leading power factor so make very sure that you don't add enough capacitance to over ride the AVR and raise the no load volts more than a few volts above nominal. Some alternators will go way over volts if you add too much capacitance. You may be able to use more capacitance if you keep a small load permanently on.
Unfortunately many modern devices are designed to run on grid waveform and are not very tolerant. It is highly probable that they would not have been tried on any other waveform. Try to not use the technical things while battery charging.
Unfortunately you are worse off with a highly sophisticated battery charger than with a transformer, rectifier and a large dc inductor, which would hold conduction over most of the ac cycle.
Try the careful addition of capacitors and see what improvement if any it makes.
Flux
