## 2 Methodology
### Case Study in Two Cities with Different Solar Radiation
#### 2.2.3 Objective Functions
On the basis of the standard BS EN 15459-1 [44], the value can be calculated using Formula (4):  
\[\text{LCC}=dIC+PWF\cdot ECC \tag{4}\]  
where \(dIC\) is the difference in investment cost between the optimization scheme and benchmark building (CNY/m\({}^{2}\)), \(PWF\) is the present worth factor in the life cycle, and \(ECC\) is the annual building energy consumption cost (CNY/m\({}^{2}\)); the CNY-USD (EUR) exchange rate is \(\sim\)0.137 (0.126). ECC includes the corresponding cost of energy consumption for heating and cooling, calculated as shown in Formula (5):  
\[\text{ECC}=Q_{H}\cdot P_{H}/H\cdot\eta_{H}+(Q_{C}/\eta_{C}-E_{PV})\cdot P_{E} \tag{5}\]  
where \(Q_{H}\) is the annual heating load (kW\(\cdot\)h/m\({}^{2}\)), \(P_{H}\) is the price of coal (750 CNY/ton), \(H\) is the electric conversion coefficient of coal (8.14 kW\(\cdot\)h/kg), \(\eta_{H}\) is the efficiency of the heating system (0.81; pipe network efficiency of 0.92 and boiler efficiency of 0.88), \(Q_{C}\) is the annual cooling load (kW\(\cdot\)h/m\({}^{2}\)), \(\eta_{C}\) is the efficiency of the cooling system (3.0), \(E_{PV}\) is the annual power generation of the photovoltaic system (kW\(\cdot\)h/m\({}^{2}\)), and \(P_{E}\) is the electricity price (0.49 CNY/kW\(\cdot\)h). PWF is used to convert the future value of funds to the present value, and the calculation method is expressed in Formulae (6)-(8) [45]:  
\[\text{PWF}=(1-(1+r_{e})^{-n})/r_{e} \tag{6}\]  
\[r_{e}=(r-e)/(1+e) \tag{7}\]  
\[r=(r_{i}-f)/(1+f) \tag{8}\]  
where \(r_{e}\) represents the market rates that take into account the rising value of energy (%), \(r\) is the actual rate (%), \(e\) is the rate of increase in energy prices (1.2%), \(n\) is the life-cycle span (30 years), \(r_{i}\) is the nominal interest rate (7%), and \(f\) is the inflation rate (2%). Taking optimization measures to reduce buildings' energy consumption may have a negative impact on the indoor thermal environment. Therefore, the percentage of annual thermal discomfort hours in a full year (i.e., 8760 h) is used as an indoor thermal environment evaluation index. Although the relevant standards specify the indoor calculated temperature in winter and summer, this is mainly used to calculate the heating and cooling energy consumption, and it is not equal to the actual indoor temperature. Considering the thermal adaptability and self-regulation ability of the human body, with reference to relevant studies [46], indoor comfort is determined when the air temperature is at 1-28 \({}^{\circ}\)C, and its value can be directly output by EnergyPlus (V 9.0) software. TDHP can be calculated as shown in Formula (9):  
\[\text{TDHP}=\frac{1}{8760\cdot n}\sum_{i=1}^{n}TDH_{i} \tag{9}\]  
where TDHP is the average value of the annual cumulative thermal discomfort hours percentage for each thermal zone (%), \(TDH_{i}\) is the annual thermal discomfort hours for each thermal zone (h), and \(n\) is the number of thermal zones. The carbon emission factor (CEF) method is used to calculate buildings' carbon emissions. The CEF is a coefficient that represents the quantity of CO\({}_{2}\) and its equivalents emitted from one unit of a certain type of material or fuel. Corresponding to the calculation of life-cycle cost, the calculation of life-cycle carbon emissions includes the carbon emissions of building materials used in optimization design and the building's operating phase, as well as taking into account the carbon reduction provided by solar photovoltaic output.