This paper proposes a novel concept of a travelling-wave thermoacoustic electricity generator, which employs a looped-tube travelling-wave thermoacoustic engine to convert thermal energy into acoustic power, an ultra-compliant alternator within the engine loop to extract and convert the engine acoustic power to electricity and an acoustic stub matching technique to match the alternator to the engine. In addition, a carefully designed cold heat exchanger acts as a phase shifting inertance to improve the performance. A simple model has been developed to capture and demonstrate the physics of this new concept, while the whole system has been investigated in detail numerically by using a specialized design tool DeltaEC. Based on the current concept, a prototype has been designed, constructed and tested. It uses atmospheric air as the working fluid, a commercially available audio loudspeaker as the electro-dynamic transducer, and inexpensive standard parts as the acoustic resonator. The experimental results have verified the simplified model and the numerical simulations of the practical build. The small-scale inexpensive prototype generator produced 11.6 W of electrical power, which shows the potential for developing cheap thermoacoustic electricity generators for energy recovery from waste heat sources. It is concluded that such concept could be very attractive provided that inexpensive ultra-compliant alternators based on the standard technology used in audio loudspeakers could be developed. Finally, some guidelines have been discussed and proposed for developing such alternators.