A number of companies are developing electric power plants for aircraft, basically for powered gliders and small ultralight aircraft. In most of these designs the power plant is of secondary importance and the aircraft can fly, or better, glide considerable distances without an engine purely by its basic aerodynamic properties.
You will not see, any time soon, electric power plants in every day workhorses general aviation class aircraft just because there are still too many limitations to overcome. The main problem is power storage: liquid fuel (Mogas, AVgas or Jet fuel) has the highest energy density per weight, which is very hard to beat, except for nuclear power plants.
For an aircraft to be able to fly, the engine/propeller must produce enough thrust to accelerate the aircraft to lift-off speed and climb for a maximum of five minutes at full power (usually). Power is reduced to maximum climb power within those five minutes until the cruise altitude is reached. After that the engine is normally set between 55 to 75% power and the aircraft flies to its intended destination.
How the propeller is driven or rotated doesn't really matter, this can either be a piston or turbine engine. Recently, a number of manufacturers are experimenting with electric propulsion systems, which include hybrids too.
The main challenge for electrical flight is where and how to store the required electrical energy for the entire flight. Or find a novel way to replenish the used energy while flying.
Compared to a piston engine the electric motor has the advantage. It is small, contains no reciprocating but only rotating parts, which is comparable to a turbine.
Among others, the Chinese firm Yuneec (pronounce as: Unique) has developed and electric motor for aircraft delivering some 40 kW (54 hp) and it weighs about 20 kg. It is used in one of their aircraft and with one 85 kg, 133,2 V 100 Ah battery (13,32 kW) it can fly some 1,5 to 3 hours (this depends on configuration, weight and such), cruise is a whopping 52 kts!
Being a glider you may expect more time from one battery charge, see image. (updated: early 2013)
Battery life is expected to be around 1500 - 3000 hrs, but real world experience shows that these items have a much shorter lifespan due to varying (fast) charge/discharge cycles, resulting in chemical and thermal stresses inside of the battery. Replacement cost is expected to be around 15000 usd.
If our aircraft was flown with a Rotax 912S equipped aircraft then the engine would deliver 100 hp (74,6 kW) for five minutes (maximum take off power time limit) and this amounts to 22,4 MJ of energy.
After that, if the aircraft flies for an hour at 75 %, the power is 100 hp times 0,75 equals 75 hp or 56 kW (energy: 201,4 MJ). So for this hypothetical flight the amount of energy needed is 201,4 MJ + 22,4 MJ totaling to: 223,8 MJ. Of course, the energy efficiency of an intern combustion engine is on average about 30% and electric aircraft (85% efficient) would need a third of the 223,8 MJ which is around 88 MJ to do the same.
Conversions: 1 J = 1 W.s (1 w = 1 J/s) and one (1) kilowatt per hour is 3600 kJ of energy (3,6 MJ) and 1 hp is 746 W or 746 J/s
An 100 Ah Lithium Polymer or Lithium Iron Phosphate (LiPo, LiFePO4) battery of 133,2 V contains some 48 MJ of energy and weighs around 85 kg, not including the controller (~10 kg) (source: Yuneec).
If we would take 100 kg of fuel (139 L mogas) then our Rotax 912S can fly around for 8+ hours at 17 L/h with 75 % power (56 kW for 8 hours is 448 kWh of energy).
Our electric motor should also produce 56 kW at the propeller and with an efficiency of 85% that would require 66 kW power plus regulation. Total energy for the 8 hour flight is thus 528 kWh or 1900 MJ. The battery weight would be around (0,565 MJ/kg) 3300 kg.
As such you may conclude is that the energy density of the battery is much lower than of liquid fuels and therefore you will see only small two-seat electric aircraft with small battery packs with and endurance of around an hour or so.
Refueling our Rotax 912S aircraft with 139 liters of mogas will take a couple of minutes. Recharging our 3300 kg LiPo battery with 1900 MJ of energy is going to take somewhat longer. The amount of power is 1900 MJ divided by 3,6 MJ (1 kWh) is 528 kW. Running a charger from the mains power (230 V) at 16 Amps (3,68 kW) will take some 143 hours. Probably a bit longer as there are efficiency losses in the charger and battery.
To reduce the recharge time you will need a three phase mains supply to recharge the batteries. On top of that, if you want to keep flying an extra battery pack will be necessary. Supplemented with solar cells on the roof of the hanger. But I doubt if you will earn the investment back (no, not subsidized).
Batteries recharging infight by solar or photo-voltaic cells is still far away from being a real solution for real aircraft. Small experiments with very light weight and low powered aircraft are being conducted but they are not yet suitable for the market. This will require many more years of development and as progress in solar cells seem to slow down, it might never get there.