[en] This paper analyses the thermoelectric power of two- and three-terminal quantum dot devices under large thermal ΔT and voltage V biases, and their performance as thermoelectric heat engines. The focus is on the interaction between electrons, far-from-equilibrium conditions, and strongly nonlinear transport, which all are important factors affecting the usefulness of the devices. To properly characterise the thermoelectric properties under such conditions, two different Seebeck coefficients are introduced, generalizing the linear response expression. In agreement with previous work, we find that the efficiency of the three-terminal thermoelectric heat engine, as measured by the delivered power, is optimal far from equilibrium. Moreover, strong Coulomb interactions between electrons on the quantum dot are found to diminish the efficiency at maximum power, and the maximal value of the delivered power, both in the Kondo regime and beyond. (paper)