Traditional electric power systems with large centralized base load power plants have a limited ability to react rapidly to the high supply variability associated with the increasing deployment of variable and intermittent renewable energy sources (RESs). Furthermore, with current power distribution networks primarily designed for unidirectional power flow, the introduction of reverse power flows by renewable feed-in strategies has been shown to negatively impact grid stability, security and system protection. For residential grid-connected microgrids (MGs) wishing to increase their renewable generation, these issues along with economic considerations often highlight that optimal operation can only be achieved through an increased self-consumption of locally generated renewable energy. Recently, researchers have highlighted that these issues can be addressed by the application of demand side management (DSM). Broadly speaking, these DSM strategies can be considered as programs which attempt to modify flexible user demands in order to achieve objectives such as reduced energy costs or increased RES utilization. To achieve these optimal energy management goals, this thesis focuses its efforts on the application of hybrid economic model predictive control (EMPC) strategies for the DSM of small to medium sized grid-connected residential MGs, containing both local photovoltaic (PV) generation capabilities and thermal energy storage (TES) devices. In particular, the investigation exploits thermal energy storage properties of switched domestic electric water heaters (DEWHs) to optimally schedule energy demand for the minimization of MG operating costs. By considering the time varying electricity tariffs, it is shown that the implementation of EMPC is able to simultaneously target reduced electricity costs while also encouraging the self-consumption of local PV generation. Finally, to address the unavoidable presence of uncertainty in domestic hot water (DHW) user demand, the thesis additionally explores the use of stochastic and robust variants of EMPC. By explicitly considering uncertainty, these control frameworks are able to provide more robust system operation. Specifically, the work implements min-max and stochastic scenario-based frameworks, which were shown to drastically reduce the violation of user comfort constraints when compared with their deterministic counterparts.