## 3 Research Methods
### Pre-Set Data Acquisition  
The pre-set data required for this study are the load data of the electric energy, cold energy, and thermal energy of the local residents in Xikou village, Lieyu township, Kinmen county, Taiwan, the power generation of renewable energy, and the parameter values of the system. 1. The Load Data  
The load data of each energy were obtained based on the open data of the Taiwan power company [31], which used the electricity load meter of the local residents in Xikou village, Lieyu township, Kinmen county in 2017. The total annual heat energy refers to the gas consumption amount of the low-carbon island plan in Kinmen [32] and the heat-load data for each month were obtained according to the ratio of heat consumption in each month of the Energy Bureau of the Ministry of Economic Affairs [33]. The monthly air-conditioning power consumption obtained from the research results of the actual measurement of residential power consumption in Taiwan [34] were converted into cold energy load data in summer, spring, and autumn and converted into heat-energy load data in winter. Finally, the energy consumption of 24 h in a day for each season was obtained from the single-day energy load distribution curve of each season in ref. [19]. 2. The Power Generation of Renewable Energy  
The parameters such as wind speed, temperature, and sunshine intensity were obtained from the historical data of climate observations from the Central Meteorological Bureau of Taiwan [35]. The power data of wind power generation and solar power generation were obtained from Equations (21) and (22) as follows. The maximum unit capacity of solar power generation was set to 75 kWH, and the wind power generation was set to 30 kWH. The formula for wind power generation is shown in Equation (21) in accordance with the literature [4]. \[P_{WT}(v)= \begin{cases}P_{7}\times\frac{v-v_{c}}{v_{7}-v_{c}}&(v_{c}\leq v\leq v _{7})\\ P_{7}&(v_{7}\leq v\leq v_{f})\\ 0&(v\leq v_{c}\sigma v\geq v_{f})\end{cases}  \tag{21}\]  
where \begin{tabular}{c c} \(P_{WT}\): & Output power of the wind turbine (kW). \\ \(P_{r}\): & Rated power of the wind turbine (kW). \\ \(v_{c}\): & The wind speed of cut into the wind force of the wind turbine (m/s). \\ \(v_{f}\): & The wind speed of cut out of the wind force of the wind turbine (m/s). \\ \(v_{r}\): & Rated wind speed of the wind turbine (m/s). \\ \(v\): & Current wind speed (m/s). \\ \end{tabular}   
Wind power generation only can start when the wind speed is higher than \(v_{c}\). However, in order to protect the generating turbine from damage when the wind speed is too high, the generator should be turned off when the wind speed is higher than \(v_{f}\). The generation of wind power can be maximized when the wind speed is higher than \(v_{r}\) and smaller than \(v_{f}\) according to Equation (21). Therefore, it is very important to select the appropriate generator capacity according to the local wind power-generating potential. The formula for solar power generation is as follows, Equation (22), in accordance with the literature [36]. \[P_{PV}=P_{STC}\times G_{AC}\times\frac{1{+}w\times(T_{c}-T_{STC})}{G_{STC}} \tag{22}\]  
where \begin{tabular}{c c} \(P_{PV}\): & Output power of solar power (kW). \\ \(P_{STC}\): & Maximum output power of solar power generation under standard test conditions (\(kW\)). \\ \(G_{AC}\): & Sunlight intensity (W/m\({}^{2}\)). \\ \(w\): & Power temperature coefficient (\(\%\)/K). \\ \(T_{c}\): & Actual working temperature of the solar cell (K). \\ \(T_{STC}\): & Standard test condition temperature (K). \\ \(G_{STC}\): & Sunlight intensity under standard test conditions (W/m\({}^{2}\)). \\ \end{tabular} 
3. The Parameter Values of the System  
The parameter values of the system refer to refs. [25; 30], that is, RMB (V) was converted into New Taiwan Dollar (NTD) and the exchange rate was RMA:NTD = 4.5:1 and rounded to four decimal places; in addition, the electricity price of the time period refers to the electricity price table of the Taiwan Power Company [31], as shown in Table 1.