We consider the privacy-preserving problem for smart grid consumers where the adversary employs a factorial hidden Markov model based inference for load disaggregation. An online convex optimization framework is further proposed for the privacy-preserving energy management strategy design. With certain specific assumptions, the derived online energy management strategy is shown to have a sublinear dynamic regret and a sublinear dynamic fit, which means our proposed online algorithm has the asymptotic performance with the optimal offline dynamic benchmark. The performance of the design approach is finally illustrated in numerical experiments