In this article, an analytical and delay-less model for the unified power quality conditioner is proposed to improve electrical power quality in power systems. The designed model includes a shunt active filter, series active filter, and common DC link, which is capable of improving power quality parameters in different conditions. The proposed control is based on a combination of the rotating reference frame theory and least mean square method that (1) can enhance power quality, including reduction of the voltage and current harmonics, voltage flicker, and reactive power of system, and (2) has no delay in the reference current generation. The DC link is also designed in a manner that capacitor voltage has a stabilized voltage in all instants. In addition, fundamental frequency estimation is employed to control frequency changes in the control system. For testing the proposed method in the worst conditions, the electric arc furnace load based on an actual stochastic arc that can generate almost all electrical power quality parameters is taken into account for the power system. The validity of proposed method is analyzed by comparing different existing control methods of the unified power quality conditioner. The simulation results show the accuracy of the control system.