Motor Types
There are actually three types of electric motors that an electric bicycle can use. Besides the AC motor, there are two different types of DC motor--the traditional brush DC motor and the newer brushless DC--motor. These are sometimes referred to as DC and BLDC motors, respectively. A BLDC motor is a sort of hybrid, combining aspects of both AC and DC motors, but using DC power. These terms--AC, DC and BLDC--will be used in this article for convenience.
DC Motors
DC motors are the most commonly available, and have been for a long time, so it is no surprise that they are used most often when building electric bicycles. They provide a great deal of torque (turning power) when they are first started, but are not as good at constant speed control. The controller system is very simple, which makes them the most economical way to build an electric bicycle. DC motor drives can be built from off-the-shelf parts with no problems.
AC Motors
AC motors are rarely used for electric bicycles, although they are the automakers' choice for prototype fully electric cars. (BLDC motors are generally used in production hybrids.) AC motors have less torque at startup, but are much better at speed control and are quieter. The real problem is that they need inverters (to convert the battery's DC current into AC) and special control systems to regulate their speed. These parts add bulk and make AC power a more expensive option.
BLDC Motors
BLDC motors are fairly popular for electric bicycles because the motor can be easily built into a wheel hub. They are quieter, more powerful and last longer than DC motors--in large part because there are no brushes rubbing inside the motor. However, BLDC motors require specialized control circuits to properly apply the DC power, a job normally handled by brushes. Because of their many advantages, BLDC motors are being used more and more, despite their higher initial costs.
The Future
With car makers investing more money to improve battery and motor technology, there will almost certainly be a trickle-down effect to smaller personal forms of transportation like scooters and power-assisted bicycles. And given the impressive performance of the Tesla, the only electric sports car in production, the use of AC power in electric cars will probably result in similar technology becoming available for electric bicycles. Cost is the only real hurdle to be crossed for AC-powered bicycles.