## 1 Introduction  
Recently, large industrial and commercial customers have begun to participate in Smart Grid (SG) programs, for example, demand side management (DSM) and demand response (DR), to save energy costs and reduce CO\({}_{2}\) emissions. However, the domestic sector has shown less interest in SG technologies, because of their individually smaller impact on the grid and the technical difficulties in aggregating large numbers of customers [1; 2]. However, as reported by the U.S. Department of Energy, buildings consume more energy compared with other broad sectors of energy consumption, such as industry and transportation, approximately 40% compared to 30% each respectively [3]. Since domestic buildings are a very significant share of total buildings, households are responsible for a large proportion of CO\({}_{2}\) emissions, through end use of both electricity and gas (or other fossil fuel) [4]. It is therefore urgent to develop cost-effective and practical methods to control energy consumption in residential dwellings. In order to meet emission reduction targets, renewable energy has been deployed in an increasingly localised and decentralised manner, in the form of distributed generation (DG) [5]. Distributed generation has the added advantage of increasing system robustness and reducing transmission losses [6]. At building level, this takes the form of micro-generation, reducing the reliance on the grid. Energy independence can be increased still further with appropriate energy storage at building level so that local renewably generated energy can be stored until it is required, which increases the self-consumption of renewably generated energy [7; 8; 9]. Moreover, with increasing uptake of SG technologies (especially smart meter technology), electrical power in buildings can be consumed more efficiently compared with conventional buildings, through change in user behaviour and automation of building services, such as lighting and heating [10; 11]. These technologies play important roles to optimise electricity consumption at building level; however they have less impact on other forms of energy use, such as gas space heating and domestic hot water. Researchers have therefore recently begun to focus on synergies between various kinds of energy carriers such that a holistic treatment can minimise the total overall energy use. In this context, a concept called 'Energy Hub' (EH) was proposed to model various forms of energy transformation, conversion and storage considered holistically in a single entity [12]. By integrating different energy carriers, the EH model increases internal and external types of dependencies among different energy carriers. For a multi-energy system, internal dependency is managed by the system operator through applying control strategies to the infrastructures, while external dependency is due to the choice of the energy supply according to customer preferences [13]. Due to the fact that the EH model can improve the dependencies of multi-energy system, it is widely used in recent literature to model the aforementioned technologies in a domestic setting and thus solve household energy optimisation problems. A comparison of two different heat storage systems is proposed in [14] to analyse the technology and cost of heat storage systems for residential micro-CHP. In [15], an application of multi-agent systems for cyber-enabled energy management of building structures (CEBEMS) is investigated; the CEBEMS models the building cooling, heat and power zones and finally energy zones, coordinates local generation to optimise building energy usage. In [16], the Monte Carlo valuation method for Energy Hubs is proposed. Together with DSM, this method solves the system uncertainty problem and improves system flexibility. However, in [14; 15; 16], system scheduling and optimisation are only based on heat demand, and electricity demand is neglected. A multi-time scale structure rule is built to optimise a micro-grid energy system in [17].