The power supply to your workshop will have fuses or circuit breakers (often called miniature circuit breakers, MCBs), which are rated in Amperes for a given voltage. A circuit breaker is a resettable electro-mechanical switch that automatically trips if the current through it exceeds a preset threshold. Because its core component is a thermal or magnetic operated device it can accept an overcurrent situation for a pre-determined length of time. Most modern domestic premises will have type 'A' or 'B' rated circuit breakers installed, which will trip quite rapidly in an overcurrent situation. However machine tools are industrial items that will draw an overcurrent at start up for somewhat longer than the average hair dryer and for this reason a motor rated circuit breaker should be installed throughout the circuit that feeds the workshop: ideally a 'D' rated breaker but a 'C' rated breaker is acceptable. A similar situation exists with fuses; the 'motor-rated' type should be fitted. Your phase converter supplier will advise you as to which rating breaker to install as they know the time for which a given breaker will hold in, e.g. 63 Amp 'D' - they should not be much more expensive than a domestic breaker.
Returning to the average hair drier for a moment; it has three components which each have an electrical role to play. The switch is used to start or stop it in normal operation or if it is failing in service; the plug is used to disconnect it from electrical power so that one can safely take it apart; and the fuse in the plug is there to prevent an excessive current flowing and thereby protect both the user and the hairdryer. A phase converter is just the same. It needs a switch that can be operated to start and stop it in normal operation and should be immediately adjacent to it; in phase converters it is reasonable for this to be an MCB that also acts as the overcurrent device.