EHONs (Energy Harvesting Overlay Networks) satisfy stringent design requirements such as high energy-and-spectrum utilization efficiencies. However, due to open access nature of these networks, eavesdroppers can emulate cognitive radios to wire-tap legitimate information, inducing information security to become a great concern. In order to protect legitimate information against eavesdroppers, this paper generates artificial noise transmitted simultaneously with legitimate information to interfere eavesdroppers. Nonetheless, artificial noise cannot be perfectly suppressed at legitimate receivers as for its primary purpose of interfering only eavesdroppers. Moreover, channel information used for signal detection is hardly estimated at receivers with absolute accuracy. As such, to quickly evaluate impact of channel estimation-and-artificial noise cancellation imperfection on secrecy performance of secondary/primary communication in ANaEHONs (Artificial Noise-aided EHONs), this paper firstly proposes precise closed-form formulas of primary/secondary SOP (Secrecy Outage Probability). Then, computer simulations are provided to corroborate these formulas. Finally, various results are illustrated to shed insights into secrecy performance of ANaEHON with key system parameters from which optimum parameters are recognized. Notably, secondary/primary communication can be secured at different levels by flexibly adjusting various parameters of the proposed system model.