Firstly there has to be a motor in the circuit. A static converter simply cannot produce three phases on its own and so it will only power two of the three phases used in equipment such as ovens (unless they have a huge three-phase fan in them). However this point probably will not trouble most readers unless they are contemplating using welders, wire erosion machines, or plasma cutters.
Secondly the capacitance in the circuit needs to be matched to the inductance in the circuit. Unfortunately the amount of capacitance required will change as the load varies on a given machine, or as different machines are operated. This characteristic is most pronounced when the primary motor starts as it will draw up to six times the normal current for a very brief period and the capacitance must vary accordingly. Because of this the 'boost' circuit was introduced which switches in a much larger capacitance at motor start (long ago our product was named after this circuit). This boost can either be manual or automatic. The automatic circuits sense either voltage or current changes and, in the case of most manufacturers, use electromechanical contactors to switch in the additional capacitance for a short period. However in addition to the boost circuit there needs to be more ability to tune the amount of capacitance so as to match the needs of the motor. Therefore manufacturers provide a capacitor bank with multiple levels controlled by another switch so that the operator may manually select the appropriate amount of capacitance. Manufacturers also provide an ammeter or voltmeter so that an operator has a guide in choosing the correct amount of capacitance (when the ammeter reads lowest the capacitance level is probably correctly tuned - in practice the human ear is a better guide as it can fairly reliably tell when a motor is running most sweetly). By now readers can probably see a few issues with statics: they might constantly need to adjust the level setting, and unreliable automatic boost circuits can lead to chattering contactors which burn out rather quickly.
There are a number of other problems with statics that arise from all this. Thirdly, because of the way the main motor is effectively generating the third phase it will only generate about two thirds of its maximum torque. Thus it might not reach its maximum speed (especially if it has had very little margin in the machine tool's design). Fourthly the largest motor must always be started first. This is probably OK in simple lathes and mills where operators can choose to switch the suds pump on after the main drive, but certainly cannot be guaranteed in CNC machinery or indeed in many common machines with semi-automatic features (e.g. industrial washing machines). Fifth, if the motor stalls then it will start to 'two-phase' and burn out its windings more than if it had been on a regular three-phase supply.
This stalling issue is why phase converter manufacturers dislike selling statics to supply woodworking equipment.
Because of the requirement for the operator to manually tune the level of capacitance, accurate phase balancing is always doubtful and so there exists the potential for sensitive machinery to be damaged - similarly because there is a lowest level of capacitance there is a smallest size of motor. The bad reputation for statics burning out motors partly arises from this, and partly because if motors are frequently stopping & starting only two phases have to bear the load - just at the time when the motor most needs three phases it has only two available. Thus motors operated with a static phase converter can easily overheat. This is most pronounced with modern motors as, unlike older motors, they are designed with very little margin in either their electrical or thermal properties.
We think static phase converters are imperfect devices - here is why:
If after reading this you insist on buying a static then please don't say you haven't been warned. In general if you are considering a static it should only be in an engineered situation such as agricultural irrigation where all the components of the system have been selected to work with each other, and where a consistent operating pattern can be predicted.