## 2 CCHP Microgrid System  
The structure of the CCHP microgrid system is shown in Figure 1. Itcontains cold, heat and electric loads [18]. The electric power is mainly supplied by the micro-gas turbine and photovoltaic power generation system. The heat power is supplied by the waste recovered heat from both the micro-gas turbineand gas boiler, which originally consume natural gas. The coldpower is mainly supplied by the electric chiller and the adsorption chiller, which consumes the electric energy and converts the heat energy into the cold energy, respectively. The mathematic model of the photovoltaic (PV) generator is described as  
\[E_{pv}=E_{pv}^{N}\frac{G}{G_{STC}}[1+k(T_{c}-T_{STC})] \tag{1}\]  
where \(E_{pv}^{N}\) is the maximum output power of photovoltaic cells under standard test conditions (\(G_{STC}\) = 1000 W/m\({}^{2}\), \(T_{STC}\) = 25 \({}^{\circ}\)C). \(G\) is the actual light intensity; \(k\) is the power temperature coefficient of the photovoltaic cell. \(T_{c}\) is the surface temperature of the photovoltaic cell, which is close to the actual ambient temperature. The mathematic model of the micro-gas turbine (MT) is described as  
\[E_{mt}=F_{mt}\cdot\eta_{mt} \tag{2}\]  
where \(E_{mt}\) is the power generated by MT. \(F_{mt}\) is the fuel consumed by MT. \(\eta_{mt}\) is the production efficiency of MT. The mathematic model of the battery is described as  
\[E_{c}(t)=E_{STC}[1+\delta_{B}(T_{b}(t)-T_{STC})] \tag{3}\]  
\[\left\{ \begin{array}{cc}\textit{charge}:&E_{b}(t)=(1-\eta_{b})E_{b}(t-1)+P_ {c}(t)\Delta t\eta_{c}\\ \textit{discharge}:&E_{b}(t)=(1-\eta_{b})E_{b}(t-1)-\frac{P_{d}(t)\Delta t}{ \eta_{d}}\end{array} \right. \tag{4}\]  
where \(E_{c}(t)\) represents the actual capacity of the battery at time \(t\). \(E_{STC}\) represents the capacity of the battery under standard test conditions. \(\delta_{B}\) is the capacity temperature coefficient. \(T_{b}(t)\) is the surface temperature of the battery at time \(t\), approximately equal to the ambient temperature. \(T_{STC}\) is the temperature under standard test conditions [19]. \(E_{b}(t)\) represents the remaining charge of the battery at time \(t\). \(E_{b}(t-1)\) represents the remaining charge of the battery at time \((t-1)\). \(\eta_{b}\) is the self-discharge rate of the battery. \(P_{c}(t)\) and \(P_{d}(t)\) are the charge and discharge power. \(\eta_{c}\) and \(\eta_{d}\) are the charging and discharging efficiency of the battery, respectively [20]. \(\Delta t\) is the time interval. Figure 1: The CCHP system structure. The mathematic model of the thermal storage tank (TST) is described as  
\[H_{\text{{lst}}}(t+1)=H_{\text{{lst}}}(t)(1-\alpha_{\text{{lst}}})+\left(\eta_{ \text{{lst}},\text{{chr}}}H_{\text{{lst}},\text{{chr}}}(t)-\frac{H_{\text{{lst}}, \text{{dis}}}(t)}{\eta_{\text{{lst}},\text{{dis}}}}\right)\Delta t \tag{5}\]  
where \(H_{\text{{lst}},\text{{chr}}}\) and \(H_{\text{{lst}},\text{{dis}}}\) are the heat storage and heat release power in the thermal storage tank, respectively. \(H_{\text{{lst}}}(t)\) is the heat energy stored in the thermal storage tank at time \(t\). \(\alpha_{\text{{lst}}}\) is the self-loss coefficient. \(\eta_{\text{{lst}},\text{{chr}}}\) and \(\eta_{\text{{lst}},\text{{dis}}}\) are the heat storage efficiency and heat release efficiencyof TST, respectively [21]. The mathematic model of the gas boiler (GB) is described as  
\[H_{gb}=F_{gb}\cdot\eta_{gb} \tag{6}\]  
where \(H_{gb}\) is the thermal power generated from the GB. \(F_{gb}\) is the fuel consumption of the boiler. \(\eta_{gb}\) is the efficiency of the boiler. The waste heat recovery device (WHRD) recycles the heat from micro-gas turbines. The mathematic model of WHRD is described as  
\[H_{\text{{re}}}=F_{\text{{mt}}}\eta_{\text{{re}}}(1-\eta_{\text{{mt}}}) \tag{7}\]  
where \(H_{\text{{re}}}\) is the heat recovered by WHRD. \(\eta_{\text{{re}}}\) is the waste heat recovery efficiency of heat energy.