The DC optimal power flow (OPF) results are potentially inaccurate since the traditional DC model only focuses on active power balance. In order to improve the model accuracy, this paper presents a relaxed ACOPF model based on a Taylor series. The proposed model considers reactive power and offnominal bus voltages as variables. Network losses are modeled through piecewise linearization and binary variables are added to prevent fictitious losses. Relaxations of the binary variables are discussed and conditions when the relaxations are exact are proved. Simulation results show that the proposed model is a better approximation for the full AC model and is computationally more efficient verses the full AC model.