  Thermodynamic uncertainty relation, quantifying a trade-off among average
current, the associated fluctuation (precision), and entropy production (cost),
has been formulated in nonequilibrium steady state and various stochastic
systems. Herein, we study the thermodynamic uncertainty relation in generic
thermoelectric heat engines under a periodic control protocol, by uncovering
the underlying Berry-phase-like contribution. We show that our thermodynamic
uncertainty relation breaks the seminal steady-state results, originating from
the non-vanishing geometric effect. Furthermore, by deriving the consequent
trade-off relation binding efficiency, power, and constancy, we prove that the
periodically driven thermoelectric heat engines can generally outperform the
steady-state analogies. The general bounds are illustrated by an analytically
solvable two-terminal single quantum dot heat engine under the periodic
modulation. Our work provides a geometric framework in bounding and optimizing
a wide range of periodically driven thermoelectric thermal machines.
