I spent 13 years designing electronics of this exact nature: three phase induction motor reduced voltage soft starters and variable frequency AC drives. I spent the last few of those years as a VFD applications engineer helping customers select and configure this equipment for various loads and industries around the country as well.
You will not be able to build something that is cheap and safe. The voltages and currents involved are well beyond the safety margin of a hobbyiest, especially someone who is openly avoiding buying commercial units in order to save money. Don't do it!
While the theory behind AC motor control is very straightforward, the detail level work (heat sink sizing, snubbering, gate drive requirements, de-sat protection, motor overload calculations, bus capacitor protection, etc.) can be quite tricky to get down, especially with heavy duty cycling and regenerative power modes which a carnival ride will CERTAINLY be generating. I strongly caution you against trying to build something of this nature unless you have significant experience not only in microcontrollers and embedded systems design but also significant experience in power electronics and three phase circuitry. People get hurt and killed building this stuff.
My first question for you is whether speed control is really required, or if you only require a soft start up and slow down. Do you vary the speed of the motor once it is started? If not, you may be able to get away with a MUCH cheaper reduced voltage soft starter. These units act like three phase light dimmers; they only adjust the applied voltage to the motor. You will not have a lot of torque at low speeds, but with the right design of motor (NEMA class D) you can achieve exactly what you're after with a fraction of the cost and maintenance.
If you really do need to vary the full-load speed of the motor then you are more or less stuck using a variable frequency drive. As you are aware these are expensive and if you buy cheap you are likely to replace them sooner due to your high surge current (they call this "constant torque") application. What I would definitely recommend doing if this is the case would be to contact various manufacturers (Allen-Bradley, Cutler-Hammer, SAF drives, Benshaw, Yaskawa, etc.) and ask for reconditioned units. Ask for a drive capable of delivering 150% rated current for 30s (this is usually known as heavy duty) or size the drive 30-50% larger than your nominal current rating. You will also likely be running off of generator power which is notorious for being undersized and prone to brownouts and surges as the load requirements change with the state of the equipment being run. Drives don't like that (voltage sags cause current spikes as the motor starts slipping and surges can cause you to overvoltage the bus capacitors) and have a tendency to either fault out or blow up.
I am all about the little guy building something and saving a buck, but this is not the type of project to do this on. If you really want to build a three phase AC drive, start with a little 10HP 480V motor with a hand brake on a test bench. You have all the potential for experiencing the pants-filling sensation of an H-bridge failure or a bus capacitor explosion two feet from your head but without the potential lawsuits and loss of life (except perhaps your own).
This is an old thread but I thought I would add something as there seems to be a widespread misunderstanding of this and there is not much information on the web. I think the designers and manufacturers of these devices want to keep the general population in the dark. I think what most people are missing is that these "fixed field" permanent magnet alternators have an inherently poor load regulation curve. With no load the output voltage can vary from 20V at idle to well over 100V at high revolutions per minute. However as the load current is increased a magnetic field is created in the stator which is in opposition to the field of the permanent magnets. Thus even short circuited it will not produce more than 40A or so. When the short is made by an SCR with a voltage drop of 1-2V this is only about 80W. The SCR is only turned on for part of the a.c cycle as it only turns on when the battery voltage exceeds 14.4V. Before it turns on the current is being delivered to the battery and all the other loads, the SCR only turns on when the other loads cannot absorb the current. When the SCR does short the windings the current is so high the the field in the stator almost cancels out the permanent magnet field so the torque load on the engine is reduced. This may seem inefficient but remember even if the field was produced by a wound rotor with slip-rings and brushes like in a car alternator that would also require power and there would also be power lost in the regulator so it isn't as bad as would first appear.
Best Answer
The two systems have vastly different applications. Yes, there is a lot of crossover between them in some fields, but the two are more suited to certain applications.
Take motors for instance. Delta is far superior for driving motors than star. With delta you can visualize a wave circulating around the triangle, and it's that wave that turns the motor. As the wave moves around the phases it effectively drags the motor around with it. It makes motor design really simple and efficient. Not so with star, where you in essence have to try and combine three single-phase motors in together,
However, when it comes to a situation where you want to spread a load between multiple circuits or devices, and the load on each phase may not be equal (unbalanced system) then a star arrangement has massive advantages. Each branch of the star (phase) is a separate circuit in its own right. The load on each phase is specific to that phase, and they have little influence on each other.
There is also a third arrangement, which is kind of half way between a star and a delta - in this arrangement each delta phase is connected with its own completely separate transformer and there is no common neutral point. This is actually seldom seen much, but I thought I should mention it here anyway. It basically combines both the star arrangement with full isolation, so can have some safety advantages (like having an isolation transformer on a normal single-phase supply) but isn't worth the hassle of a system without a common neutral point.
To clarify what I mean about a wave rotating around a delta, here is a little animation I knocked up:
Note: It's Christmas Day, I'm drunk, and that might all have been complete gibberish for all I know.