Where can I find 1.5kWh energy, at about 5-15Wh/kg batteries that can deliver about 350kW power? (as indicated on this wikipedia article?)
I'd give a look at high discharge rate lithium ion batteries. Batteries intended for radio controlled models are perhaps the most practical source for a one-off prototype; they feature massive discharge rates, moderately high energy densities and they are relatively affordable.  

For example, a 22.2 V 0.864 kg pack of six 5 Ah 3.7 V pouch cells in series can be bought online for about $70. The pack has a 60 C continous discharge rating, meaning that you could draw 5 Ah * 60 = 300 A of current, equating to a power output of 300 A * 22.2 V = 6.66 kW.
Assembling 60 such packs together would yield a battery with a maximum continous power output of 400 kW, an energy storage capacity of 6.66 kWh, a mass of 52 kg and a cost of $4200. You would also require a custom battery management system, and a way to quickly run away when it blows up.