The operation of a thermoelectric module in heatingcooling mode, generating mode, and regenerating mode can be discussed in terms of power, cooling load, and current. A direct current machine in motoring mode and generating mode and an induction motor in motoring mode and regenerating mode are analogous to thermoelectric modules. Therefore, the first objective of this work is to present the fourquadrant (4Q) operation diagram and the 4Q equivalent circuits of thermoelectric modules in heatingcooling mode and generating mode. The second objective is to present the cooling and regenerating curves of a thermoelectric module in cooling mode and regenerating mode. The curves are composed from the cooling powers and the generating powers, the input and output current, the thermal resistance of the heat exchanger, and the different temperatures that exist between the hot and cold sides of the thermoelectric module. The methodology used to present the data involveddrawing analogies between the mechanical system, the electrical system, and the thermal system; an experimental setup was also used. The experimental setup was built to test a thermoelectric module (TE 2) in cooling mode and regenerating mode under conditions in which it was necessary to control the different temperatures on the hot and cold sides of TE 2. Twothermoelectric modules were used to control the temperature. The cold side was controlled by a thermoelectric module labeled TE 1, whereas the hot side was controlled by a second thermoelectric module labeled TE 3. The results include the power, the cooling load, and the current of the thermoelectric module, which are analogous to the torque, the power, the speed, and the slip speed of a direct current machine and an induction motor. This 4Q operation diagram, the 4Q equivalent circuits, and the cooling and regenerating curves of the thermoelectric module can be used to analyze the bidirectional current and to select appropriate operating conditions in the cooling and regenerating modes.