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The Galactic Center (GC) presents one of the highest stellar densities in our Galaxy, making its surroundings an environment potentially rich in radio transients, such as pulsars and different kinds of flaring activity. In this paper, we present the first study of transient activity in the region of the GC based on Atacama Large Millimeter/submillimeter (mm/submm) Array (ALMA) continuum observations at 230 GHz. This search is based on a new self-calibration algorithm, especially designed for variability detection in the GC field. Using this method, we have performed a search of radio transients in the effective field of view of~$\sim 30\,$arcseconds of the GC central supermassive black hole Sagittarius A* (SgrA*) using ALMA 230 GHz observations taken during the 2017 Event Horizon Telescope (EHT) campaign, which span several observing hours (5-10) on 2017 April 6, 7, and 11. This calibration method allows one to disentangle the variability of unresolved SgrA* from any potential transient emission in the wider field of view and residual effects of the imperfect data calibration. Hence, a robust statistical criterion to identify real transients can be established: the event should survive at least three times the correlation time and it must have a peak excursion of at least seven times the instantaneous root-mean-square between consecutive images. Our algorithms are successfully tested against realistic synthetic simulations of transient sources in the GC field. Having checked the validity of the statistical criterion, we provide upper limits for transient activity in the effective field of view of the GC at 230 GHz.