What battery specifications to look for, to run the following setup?
Well, let's run some numbers!

We will start with 1HP = 745.7W. Therefore, each of your motors requires 7.46KW in order to run. You have 3 of them, so you need to supply 22.38KW in order to run them all full blast.

You specify 7 hours, so that gives us 156.6KWh that you need to have as your battery capacity. Now, we can look at some common chemistries of batteries to get an idea of their energy density and how much they would weigh (source):

NiMH: 95Wh/kg

NiCad: 39Wh/kg

Li-Ion: 128Wh/kg (LiPos are in the range of 100-265Wh/kg as well)

Let's choose some LiPos at 150Wh/kg. Given that you need 156.6KWh, this means your battery will need to be 1044kg. That is far too heavy given your 50kg limit, obviously. For your battery to weigh, for example, 25kg, you would need to find energy storage that has a density of 6264Wh/kg. I don't think anything exists like that presently.

Now, there are compromises we can make:


If you can chop down your run time, you can reduce the size of your battery proportionally.
Your motors will not be running full blast all the time. It is unreasonable to think that a brushless motor would need 7457W just to even spin. Calculate, based on your flight characteristics, the average power that you would need to supply to your motors to hover (or whatever). Your copter won't need to ascend forever, so hovering might be a reasonable average compromise. I suspect that it will be much smaller, maybe even 30%-50% of what you have now.


I'm sure there are more (its your copter to design!). Once you have made some compromises, run the "back of the napkin" numbers again to see how big of a battery you would need. You need to cut at least 90% of your power requirements to even get into the range of current technology with a 25kg battery (6264W/kg down to 626W/kg), or you can increase the maximum weight of your copter.

The other thing you will need to consider is your battery structure. You say that you need 120V for these motors to run. If that is the case, you will need to have at least 33 LiPo batteries in series (assuming nominal 3.7V) to get that high. This voltage will vary during the charge cycle of the battery from 99V to 138.6V as well. The other factor to consider is the discharge rate of your batteries. At 120V, 30HP, you will need to supply 186A. Most LiPo batteries can sustain 30-50C (C = the charge size of the battery, for example a 2Ah battery would sustain 60A if it was rated for 30C), so you will need to put several stacks of 33LiPos in parallel in order to avoid overheating and blowing up your batteries (so they share the load). The number of parallel stacks will also be influenced by your required battery size (in Ah). The charging setup for this would start to look very similar to  a BMS in an electric vehicle such as a Nissan Leaf since you have so many cells to charge and would probably need to be custom built.

Again, if you make compromises it is possible. If your motors are not running full blast, you don't need to supply 186A continuous, thus reducing the number of parallel stacks you need to meet your current requirements.