Is my homebrew Eldritch Invocation that emulates the sleep spell balanced?

I’ve been inspired to make an Eldritch Invocation for warlocks that allows you to use the damage from eldritch blast, and make use of it like the dice rolled for sleep:

Eldritch Slumber

Prerequisites: eldritch blast cantrip

When you cast eldritch blast, instead of rolling 1d10 per beam, you make any spell attacks as normal and roll 2d10 per beam (plus any additional modifiers from additional abilities or critical hits). Rather than deal damage, the number rolled per beam is instead the number of hit points of creatures that beam can affect. You may target the same creature with additional beams, but the effects do not stack.

All affected creatures are rendered unconscious, until a number of rounds have passed equal to your charisma modifier, the sleeper takes damage, or someone uses an action to shake or slap the sleeper awake.

Balance Assessment

I think this is balanced because while you do not affect many creatures, you can cast it at will. At higher levels, this scales but should not past the usefulness of the original cantrip.

It also feels like where sleep affects 5d8+2d8/level, other damaging effects of the same level deal half as much damage. It stands to reason if eldritch blast deals 1d10+1d10/4 levels, sending twice as many hit points of creatures to sleep is fair, but still behind what sleep can do.

I’ve tried to word it so that you can’t stack beams together, but I don’t know if that is too big of a nerf. Also as Eldritch Blast doesn’t have a duration, I have supplied one.