Duty-cycle scheduling is an effective way to balance energy consumptions and prolong network lifetime of wireless sensor networks (WSNs), which usually requires a connected dominating set (CDS) to guarantee network connectivity and coverage. Therefore, the problem of finding the largest number of CDSs is important for WSNs. The previous works always assume all the nodes are non-rechargeable. However, WSNs are now taking advantages of rechargeable nodes to become energy harvest networks (EHNs). To find the largest number of CDSs then becomes completely different. This is the first work to investigate, how to identify the largest number of CDSs in EHNs to prolong network lifetime. The investigated novel problems are proved to be NP-Complete and we propose four approximate algorithms, accordingly. Both the solid theoretical analysis and the extensive simulations are performed to evaluate our algorithms.