## 3 Results
### Stochastic Load Simulation  
In order to implement the stochastic load simulation for the rural residential building, it is first necessary to determine the specific parameters corresponding to the stochastic model of indoor temperature in Section 2.1. Among them, the setting of transfer probability in the Markov chain model mainly referred to the literature [30], which has been studied in detail for the use of rural residential buildings in northern China. The range of values for the indoor temperature in each room corresponding to different occupancy and activity situations is shown in Table 2.  
Based on the stochastic model of indoor temperature, random indoor temperature scenarios in each room were obtained by sampling. The results of a single simulation are shown in Figure 4. As can be seen from Figure 4, the simulation results of the stochastic model of indoor temperature in this study can reasonably reflect the usage characteristics of the four rooms in the rural residential buildings. Among them, the hall and kitchen, which take on the functions of daily activities and cooking, respectively, are occupied mainly during the day, so their indoor temperatures are set lower at night. The second bedroom, which takes on the function of sleeping, is mostly occupied at night, so its indoor temperature is generally set lower during the day. And the master bedroom, which simultaneously performs the functions of sleeping and daily activities, may be occupied throughout the day. At the time of occupancy, the indoor temperature at night is lower than that in the daytime, reflecting the distinction between sleeping and daily activities.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Occupancy Scenario** & **Room** & **Temperature Settings** \\ \hline \multirow{3}{*}{if \(O_{p}(t)=1\) :} & Master bedroom, & \(T(t)\sim U(11,\ 14)\)\textasci{C}, if \(1\leq t<8\) or \(22<t\leq 24\)h \\  & second bedroom & \(T(t)\sim U(15,\ 18)\)\textasci{C}, if \(8\leq t\leq 22\)h \\  & Hall & \(T(t)\sim U(15,\ 18)\)\textasci{C}, \(0\leq t\leq 24\)h \\  & Kitchen & \(T(t)\sim U(15,\ 18)\)\textasci{C}, \(0\leq t\leq 24\)h \\ \hline \hline \end{tabular}
\end{table}
Table 2: The parameters of the stochastic model of indoor temperature.  
Figure 4: Simulation results from the stochastic model of indoor temperature in rural residential buildings. (Note: Light yellow area indicates that the room is occupied at this time).  
In order to implement the stochastic load simulation for the rural residential building, it is also necessary to determine the 24 h outdoor design conditions. Harbin's wintertime indoor-outdoor temperature difference is so great that variations in the outdoor temperature has little effect on the building's peak load. Thus, it is assumed in this study that the outdoor dry bulb temperature will remain constant over time. On this basis, the 24 h outdoor design conditions were determined based on the extreme value of the dry bulb temperature in Harbin provided by the code [7].  
Following the steps in Section 2.2, a stochastic simulation of the heating load in the rural residential building was carried out in combination with the indoor temperature scenarios and outdoor design conditions. In order to determine the minimum number of simulations, the rate of change in the mean value of the design load samples at different simulation times was calculated according to Equation (8), and the specific results are shown in Figure 5. From Figure 5, it can be seen that when the number of simulations reaches 550, the rate of change \(S(N)\) is less than 0.2%. At this point, the convergence criterion is reached.