## Inner Layer Modeling and Optimization
### Modeling of Energy Hub  
An EH integrates a variety of energy converters, such as compressors, _CHP_, heat exchangers, CCHP, heat recovery devices, transformers, microturbines, power-electronic devices, gas boilers, fuel cells, and other equipment, where the inputs and outputs of multiple energy flow are usually available [12; 18; 19]. From a system point of view, an EH is considered a unit where multiple energy flows can be converted, conditioned, and stored. This EH is also able to provide the basic features, such as input and output, conversion, and diversified storage of different energy forms [7; 10; 17; 18; 19]. A general model showing couplings with multiple inputs and outputs is illustrated in Figure 1. A unit is structured where multiple inputs are converted into multiple outputs [7; 19; 21]. This conversion can either be established by a single device or by a combination of multiple converters, it follows from Figure 1 that:  
\[\underbrace{\left[ \begin{array}{c}L_{e}\\ L_{h}\\ \vdots\\ L_{0}\end{array} \right]}_{\text{L}}=\underbrace{\left[ \begin{array}{cccc}C_{ \alpha\alpha}&C_{\beta\alpha}&\cdots&C_{0\alpha}\\ C_{\alpha h}&C_{\beta h}&\cdots&C_{0\alpha}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ C_{\alpha 0}&C_{\beta 0}&\cdots&C_{00}\end{array} \right]}_{\text{C}} \underbrace{\left[ \begin{array}{c}P_{\alpha}\\ P_{\beta}\\ \vdots\\ P_{0}\end{array} \right]}_{\text{P}} \tag{1}\]  
where **L** and **P** stand for the steady-state output and input powers vectors, respectively; the matrix **C** is called converter coupling matrix; the coupling factor \(C_{ij}\) defines the coupling between input and output power flow. The economic efficiency of an EH can be achieved by optimally dispatching different energy carriers [21; 22]. Real facilities that can be considered as EHs are, for example, small isolated energy systems, demonstration project parks, industrial areas (steel works, paper mills), big building complexes (schools, hospitals), and business areas (shopping malls). Based on the planning and requirement of the integrated energy supply in a high-tech industrial development zone in north China, the EH architecture is constructed in Figure 2. The EH mainly includes wind power, various types of energy storage equipment, _CHP_ units, _P2G_, _P2H_, etc., while three main energy systems (electrical, natural gas, and thermal) are considered as inputs of the EH, e.g., out of the industrial development zone. Electricity, steam/heat water, cold water, and gas will be allocated to the users of a high-tech industry development zone economically and reasonably through the energy conversion equipment. The various kinds of energy imported to an EH will be assigned, stored, and converted to meet the requirement of different energy end users. In the following, the main energy conversion equipment, including wind power, various types of energy storage equipment, the _CHP_ unit, _P2G_, _P2H_, are modeled and introduced, respectively. A wind power unit refers to small wind farms including many types of wind turbines and, in this paper, the relation between wind speed and the generated power from the wind turbine [1; 3; 20; 24] is formulated as:  
\[P_{wind}^{t}=\left\{ \begin{array}{ll}0&\quad v^{t}<v^{in}\,and\,v^{t}>v^{out }\\ P_{wind}^{num}\cdot\frac{v^{t}-v^{in}}{v^{num}-v^{in}}&\quad v^{in}\leq v^{t}<v^{ nom}\\ p_{wind}^{nom}&\quad v^{nom}\leq v^{t}\leq v^{out}\end{array} \right. \tag{2}\]  
where \(P_{wind}^{t}\) denotes the power produced by the wind turbine; \(v^{t}\) stands for the wind speed; \(P_{wind}^{nom}\) represents the wind turbine rated power; \(v^{in}\) represents the cut-in wind speed for the wind turbine; \(v^{nom}\) stands for the wind turbine rated speed; and \(v^{out}\) denotes the cut-out wind speed for the wind turbine. In most cases, energy storage technology has been utilized in micro-grids, distributed energy systems, and multiple energy integration systems to smooth the fluctuations caused by PHEVs, renewable energy sources.