Constant power loads are generally converter interface loads and they have negative impedance effects.
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The explanation is quite straightforward. With the constant power load if the bus voltage drops then the current increases which further reduces the bus voltage and so on. So it is very destabilizing and leads to the collabse of the bus voltage.

Now if i have an induction motor load and i have voltage regulation over the inverter, how well will it work if there is a cluster of loads fed by inverters?

they have a drawback as tightly regulated power electronic converters
tend to show negative impedance characteristics because of their characteristics similar to a constant power load and they leat to instability of power systems.
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