Today, as a consequence of the growing installation of efficient technologies, such as combined heat and power (CHP) as a co-generation, the integration of electricity through grid supply, Photovoltaic (PV) and energy storage systems as an integrated network is attracting a lot of attention in smart grid applications. To model the interaction among electricity and natural gas, the energy hub framework is adopted to determine a modelling procedure for such multi-carrier energy systems. This paper presents a residential energy hub model for a smart home as a modified framework of conventional energy hubs in a smart grid with consideration of heat pump water heater, coordination of sources and carbon emissions. Therefore, this study is twofold; the first part optimizes the operation of the combined CHP, Photovoltaic and storage system under dynamic pricing. Since residential load management plays a key role in realizing household demand response programs in a smart grid, performing optimal load management in the proposed residential energy hub model is also studied in this paper. To achieve this, the optimization problem is extended by considering modelling of a heat pump water heater. It is also found out that CO2 signal could give customers an environmental motivation to shift or reduce loads during peak hours, as it would enable co-optimization of electricity consumption costs and carbon emissions reductions.