## 3 System Structure
### Calculation Methods  
The relevant index about economic saving is one of the most important factors in the investigation of the DHW system. The economic assessment provides information on how the economic resources (investments, fuels, etc.) are used to meet the customer requirements. Compared with traditional energy acquisition methods, micro-CHP system has usually higher initial investment and lower running costs compared with the conventional energy supply system, which serves the electricity load by utility grid and thermal load by gas boiler. Therefore, in economic evaluation, an important index, cost-saving ratio [23], has been employed. The index takes into account more factors. It expresses the profitability of the micro-CHP system and is defined as the ratio of difference between the new system and the conventional system (GB) to the annual energy cost of the conventional system, as shown in (1). Its size indicates the cost-saving capacity of the CHP system. \[CSR=(\frac{C_{CON}-C_{i}}{C_{CON}})\times 100\% \tag{1}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Unit** & **Value** \\ \hline Rated power output & kW & 25 \\ Rated power output & kW & 25 \\ Heat power output & kW & 38.5 \\ Gas consumption output & kW & 74.6 \\ Power generation efficiency & \% & 33.5 \\ Heat efficiency & \% & 51.5 \\ Comprehensive efficiency & \% & 85 \\ Frequency & Hz & 50 \\ Voltage & V & AC400 \\ Maximum temperature of water inlet & \% & 85 \\ Water inlet flow & L/min & 110 \\ Supply pressure for fuel gas & kPa & 1.5-3.0 \\ Dimensions (height \(\times\) width \(\times\) depth) & mm & \(2060\times 2150\times 800\) \\ Ambient temperature & \% & \(-5\)°C-40 °C \\ Relative humidity & \% & 80 or less \\ Altitude & m & 2000 or less \\ Low heating value (LHV) & MJ/Nm\({}^{3}\) & 35.588 \\ Generator Type & & Compact and light weight permanent \\  & & magnet generator \\ Grid connection method & & High efficiency inverter grid connection \\ Output heat exchanger & & Stainless steel with brazed plate construction \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of the internal combustion engine. Figure 1: The CHP system flow chart. \[NPV=-C_{i}^{initial}+\sum_{j=1}^{n}\frac{C_{i}^{Save}}{(1+\alpha)^{j}} \tag{2}\]  
\[payback=\frac{C_{i}^{initial}}{C_{i}^{Save}} \tag{3}\]  
where CSR is cost-saving ratio, \(C_{CON}\) and \(C_{i}\) are the annual average investment costs for GB and other systems, \(C_{i}^{initial}\) and \(C_{i}^{Save}\) are initial investment the annual saving cost each system. NPV is net present value. The payback period is the ratio of the initial investment to the amount of cost saved. \[C_{CON}=C_{CON}^{Inv}+C_{CON}^{Gas}+C_{CON}^{OM} \tag{4}\]  
\[C_{CON}^{Inv}=\frac{C_{Boiler}^{initial}\times(1+\alpha)}{n_{CON}} \tag{5}\]  
where \(C_{CON}^{initial}\), \(C_{CON}^{Inv}\), \(C_{CON}^{Gas}\) and \(C_{CON}^{OM}\) are respectively initial investment, annualized investment cost, annualized gas consumption cost and annualized operation and maintenance cost, for GB. \(n_{CON}\) is the lifetime of GB, \(\alpha\) is an estimated net residual value rate, j is the number of years. \[C_{i}=C_{i}^{Inv}+C_{i}^{Gas,or,Ele}+C_{i}^{OM}-C_{i}^{in} \tag{6}\]  
\[C_{i}^{Inv}=\frac{C_{i}^{initial}\times(1+\alpha)}{n_{i}} \tag{7}\]  
\[C_{i}^{Ele}=\sum_{t=1}^{t=8760}Q_{i,t}\times P_{t}^{Ele} \tag{8}\]  
\[C_{i}^{Gas}=\frac{\sum_{t=1}^{t=8760}Q_{i,t}\times P_{t}^{Gas}}{LHV} \tag{9}\]  
Figure 1:0  
Figure 1:1  
where \(C_{i}^{initial},C_{i}^{Inv},C_{i}^{Gas},C_{i}^{Ele},C_{i}^{OM},C_{i}^{Save}\), \(C_{i}^{in}\) and \(Q_{i}\) are respectively initial investment, annualized investment cost, annualized gas consumption cost, annualized electricity consumption cost, annualized operation maintenance cost, annualized saving cost, annualized electricity revenue from grid and actual heat supplied per hour, for one of the CHP, domestic gas-fired heater, domestic electric heater and ASHP. \(n_{i}\) is the lifetime of one of those.