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Power electronic based loads often behave as constant power loads, especially when feeding machine or actuator drives under current and speed control. The constant power loads (CPL) can affect the stability of the power system. The problem is a particular issue in aircraft power systems as the proportion of CPLs increases with the advent of the more-electric aircraft. This paper deals with stability analysis of a three-phase frequency-wild AC power system with CPL fed through six-pulse diode rectifier. The mathematical model of the power system suitable for stability analysis is derived using DQ-transformation method. Simulation results are used to verify the theoretical results. It is also shown how the theory can be used to predict instability due to possible variations in system parameters.