Due to cyber-physical fusion and nonsmooth characteristics of energy management, this article proposes a security event-trigger-based distributed approach to address these issues with developed smoothing technique. To tackle with nonconvex and nondifferentiable issue, a randomized gradient-free-based successive convex approximation is developed to smooth economic objective function. Due to resilience ability against security issue, a security event-triggered mechanism-based distributed energy management is proposed to optimize social welfare, which coordinately controls both power generators and load demand. The security event-triggered mechanism is designed to reduce power system security risks, and relieve communication burden caused by smoothing calculation, the convergence of proposed distributed algorithm is also properly proved. According to those obtained results on both IEEE 9-bus and IEEE 39-bus systems, it reveals that the proposed approach can achieve good convergence performance and have less security risks than other alternatives, which also proves that the proposed approach can be a viable and promising way for tackling with energy management issue of cyber-physical isolated power system.