Traditional power flow algorithms assume that a slack bus is present and that the frequency is not fluctuating. In islanded industrial systems and microgrids, however, these assumptions are not valid because such systems usually do not have a strong source performing as the slack bus and the system frequency is more prone to vary near nominal frequency. Considering these characteristics, this paper presents a novel universal power flow (UPF) algorithm for industrial systems and microgrids as well as traditional systems, with a focus on active power. Development of a reactive power UPF algorithm will be presented in a subsequent paper. The proposed UPF model has the following merits: first, it can handle islanded and grid-connected systems at nominal or off-nominal frequency; second, it can handle the active control strategies of distributed generators (DGs), such as isochronous (ISOC) control, droop control, or constant power control; third, it can handle the megawatt and megavolt-ampere reactive limitations of ISOC or droop DG units; fourth, it can evaluate system frequency; and finally, it can handle frequency-dependent active and reactive power loads. The proposed UPF model is validated by comparing the results with those obtained from a real-time simulator.