Ambient energy-harvesting technology is a promising approach to keep wireless sensor networks (WSNs) operating perennially. Depending on the harvesting source, nodes can either be active (alive) or inactive (dead) at any instant in such Energy-Harvesting WSNs (EH-WSNs). Thus, even in a static deployment of EH-WSNs, the network topology is no longer static. A popular method to increase energy-efficiency in WSNs is by employing topology control algorithms. Most of the topology control algorithms in the literature focus only on the transmission power while constructing a static topology without taking into account the residual energy of the nodes. Consequently, they cannot handle the situation when nodes have different energy levels, and when the number of active nodes varies with time in EH-WSN. Since the number of nodes alive in EH-WSNs is varying there is no possibility of having a centralized solution. To address this issue, we present two localized energy based topology control algorithms, viz., EBTC-1 and EBTC-2. EBTC-1 is for convergecast applications of WSNs and EBTC-2 is for a generic scenario where all nodes are required to be strictly connected. In some cases, to ensure fault tolerance the network may be required to be k-connected. While typical topology control algorithms select a particular number of neighbors, the distinguishing feature of both these algorithms is that they select neighbors based on energy levels, and render the global topology strongly-connected. Simulation results confirm that EBTC-1 and EBTC-2 reduce the transmission power and they let nodes have neighbors with high remaining energy. Results show that our proposed algorithms increase at least 33% in the remaining energy per neighbor. In addition, in terms of energy consumption and fault-tolerance, our proposed algorithms typically achieve 1-connected topology using 74% less energy compared to K-Neigh.