The overwhelming demand for data by an ever-increasing number of users is a great challenge wireless cellular networks are faced with. One potential solution to this issue is deploying a massive number of small cells (SCs) in the existing macro network. As SC overlay has a big role in the future wireless networks that can overcome the data traffic upsurge at little power cost, heterogeneous network (HetNet) has been viewed as a promising technology for 5G networks that extends cell coverage, improves network capacity and offloads the network traffic from the macro cell (MC) to the SCs. However, the hyper-dense SCs and their uncorrelated operation raise an important question about the joint power consumption of the macro base station (MBS) and the small base stations (SBSs) in the HetNet since the aggregate power consumption of the dense SBSs cannot be ignored. Recently, the SC sleeping technique has become a hot topic for saving energy in HetNets. To minimize power consumption in HetNets, we propose three algorithms to dynamically adapt the operation of the SBSs to active/sleep (on/off) for non-uniform user distribution in the HetNet. We investigate the general optimal power minimization problem for HetNet that requires relatively high computational complexity. Taking into account the additional increase of the traffic load brought to the MBS, a key design principle of the proposed algorithms is to switch off the SBSs gradually based on their locations, user densities in their coverage areas or the highest power that can be saved by switching some of them off, respectively. Then, we enhance the mathematical framework to make the analysis more realistic by considering the offloading between the SCs and the MBS that occurs when the traffic load exceeds SCs' capacity. In this paper, based on the fact that user densities of SCs and MC change with time, we model the traffic on the European traffic profile and portray the power consumption of the HetNet throughout the day. Simulation results show that by applying SC sleeping and our proposed algorithms, the HetNet can save about 20% power daily. The performances of our proposed algorithms are close to that of the optimal algorithm and their computational complexities are remarkably lower.