The article incorporates an analysis of the switching-on process of alternating current (AC), low-voltage (LV), and electromagnetic (EM) relays energized by harmonically polluted voltage sources. In the undertaken research, the dynamic parameters of relays actuated by electromagnetic drive were examined for shape and supply voltage waveform distortion levels as described by different THD factor values. During the research, diverse supplying voltages were delivered to drive electromagnet coils at a variety of phases so as to reflect the stochastic nature of the energizing procedure. The performed analysis allowed for determining the most influential and decisive factors dictating the basic parameter values of the switching-on process. As an outcome, time-related parameters of relay moving armature movement were obtained, and the frequency of disorder occurrences during the switching-on was examined. For experimentation needs, an experiment stand was developed, and dedicated software for measurement results analysis was elaborated. Based on the study results, EM relay switching-on operation reliability was evaluated in view of electric energy quality.