The onset of self-excited oscillations is developed theoretically for a traveling wave thermo-acoustic-piezoelectric (TAP) energy harvester. The harvester is intended for converting thermal energy, such as solar or waste heat energy, directly into electrical energy without the need for any moving components. The thermal energy is utilized to generate a steep temperature gradient along a porous regenerator. At a specific threshold of the temperature gradient, self-sustained acoustic waves are generated inside an acoustic resonator. The resulting pressure fluctuations excite a piezoelectric diaphragm, placed at the end of the resonator, which converts the acoustic energy directly into electrical energy. The pressure pulsations are amplified by using an acoustic feedback loop which introduces appropriate phasing that make the pulsations take the form of traveling waves. Such traveling waves render the engine to be inherently reversible and thus highly efficient. The behavior of this class of harvesters is modeled using the lumped-parameter approach. The developed model is a multifield model which combines the descriptions of the acoustic resonator, feedback loop, and the regenerator with the characteristics of the piezoelectric diaphragm. A new method is proposed here to analyze the onset of self-sustained oscillations of the traveling wave engine using the classical control theory. The predictions of the developed models are validated against published results. Such models present invaluable tools for the design of efficient TAP energy harvesters and engines.