Effects of low voltage on power grids?
If you read into major blackouts in history (which have been attributed to cascading effects) - e.g. the 2003 Italy blackout or the 2003 US Northeast blackout, you'd see that the common pattern is that the changes to the grid load were too quick for reactive action. It's not that the undervoltage or underfrequency itself was the problem, because you can always shed load as to restore the balance between generation and consumption, and provision enough spare capacity to cope with yet more failures should they happen to arise. However if you don't act quickly enough, the load that has been shifted to other power lines or generating stations can cause further problems, exacerbating the issue.
Also see this: If a large AC generator is overloaded, will it lose frequency or voltage?
I think most power plants are constructed in a way that the electrical generator is undersized with respect to the prime mover (likely because you don't want to be able to stall it at full power!). So you're more likely to lose voltage than speed unless the overloading of the grid is particularly severe.
Yet another aspect is that not all power input to the grid is via synchronous generators. Solar power uses inverters. You may want to dismiss them as insignificant, but they are a significant % of generation in some countries. In yet another countries you may have HVDC links to neighbouring grids, and if you view these as a &quot;power producer&quot;, their generation can also be quickly ramped up without losing frequency (whether the other grid will like it is a different story though, you only see the DC so you don't care).