Energy harvesting has become a promising and alternative solution to conventional energy generation patterns to overcome the problem of supplying autonomous electrical systems. More particularly, thermal energy harvesting technologies have drawn a major interest in both research and industry. Thermoelectric Generators (TEGs) can be used in two different operating conditions, under constant temperature gradient or constant heat flow. The commonly used TEG electrical model, based on a voltage source in series with an electrical resistance, shows its limitations especially under constant heat flow conditions. Here, the analytical electrical modeling, taking into consideration the internal and contact thermal resistances of a TEG under constant temperature gradient and constant heat flow conditions, is first given. To give further insight into the electrical behavior of a TEG module in different operating conditions, we propose a new and original way of emulating the above analytical expressions with usual electronics components (voltage source, resistors, diode), whose values are determined with the TEG's parameters. Note that such a TEG emulation is particularly suited when designing the electronic circuitry commonly associated to the TEG, to realize both Maximum Power Point Tracking and output voltage regulation. First, the proposed equivalent electrical circuits are validated through simulation with a SPICE environment in static operating conditions using only one value of either temperature gradient or heat flow. Then, they are also analyzed in dynamic operating conditions where both temperature gradient and heat flow are considered as time-varying functions.