## 4 Simulation Results and Discussion
### Case 1: MES in Office Buildings  
A typical day is chosen to support the details of the research, the period of MPC based scheduling is 24 h and \(\Delta\)\(t\) is 1 h. The office arrival time of EVs owners is represented by a normal distribution with mean value 9:00 a.m. and standard deviation 1 h; and the office departure time follows a normal distribution with mean value 6:00 p.m. and standard deviation 1 h. The scenarios of the available number of EVs at each time are generated by scenarios generation and reduction technique. It is assumed that the thermal power demand is completely dependent on the CHP units without additional equipment [41; 42]. The capacity of each EV is assumed to be 48 kWh, and the total number of available EVs is 100 in this case. The lower and upper limits of aggregated SOC are set to be 0.3 and 1. The TOU pricing for electricity consumption and the fixed price for natural gas are shown in Table 1, in which four different electricity prices during a day are considered.  
Two thousand scenarios are generated by using the LHS method and the number of scenarios is further reduced to 10 by using the scenario reduction technique. The reduced scenarios \(\{DAN^{s}(1),\cdots,DAN^{s}(T)\},s\ =\ 1,\cdots,10\) are depicted in Figure 7 and the probabilities of the reduced  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Item**} & **Valley** & **Flat** & **Peak** \\  & **(00:00 a.m.–7:00 a.m.)** & **(8:00 a.m.–10:00 a.m.,** 7:00 p.m.–11:00 p.m.)** & **(11:00 a.m.–6:00 p.m.)** \\ \hline Electricity from main grid & 0.3539 RMB/kWh & 0.7785 RMB/kWh & 1.2283 RMB/kWh & 1.3377 RMB/kWh \\  & & Case 1 & \\ Price of Gas & & 3.4 RMB/m\({}^{3}\) & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Energy tariff in Case 1.  
scenarios are given in Table 2, the sum of which is equal to 1. It is discovered from Figure 7 that most of the EVs arrive in office buildings at 9:00 am., and most of the EVs\({}^{\prime}\) owners get off work when \(t\) = 6:00 p.m.  
The electrical and thermal demands during 24 h are depicted in Figure 8a, b respectively. When it is 8:00 a.m., the electricity demand begins to increase; during 12:00 p.m.-1:00 p.m. have a slight drop, and after 6:00 p.m., the demand begins to fall steadily. The thermal demand is higher during the time period 9:00 a.m.-6:00 p.m.  
The electricity and thermal scheduling results are shown in Figures 9-11. The aggregated SOC of EVs is drawn in Figure 12. During the period 8:00 a.m.-12:00 a.m. and 1:00 p.m.-6:00 p.m., with the relatively higher electricity price and more available EVs, there is no electricity purchasing from the connected main grid, and the thermal and electric demands are satisfied by the CHP units and EVs. Even during the period 12:00 a.m.-1:00 p.m., the electricity generations from CHP units can not only provide all the electric demand, but also charge the EVs, making its aggregated SOC rise a little during the steady descending process shown in Figure 12. No purchasing electricity power from extern main grid during the period of higher price shows an expected economic efficiency. During the period 9:00 a.m.-8:00 p.m. when the electricity and thermal demands are higher, as CHP_I with a fixed heat-to-electricity ratio has a higher energy conversion efficiency compared with CHP_II,  
\begin{table}
\begin{tabular}{l l l l l l l l l l l} \hline \hline
**Scenarios** & **s1** & **s2** & **s3** & **s4** & **s5** & **s6** & **s7** & **s8** & **s9** & **s10** \\ \hline probabilities & 0.075 & 0.060 & 0.151 & 0.075 & 0.110 & 0.089 & 0.082 & 0.142 & 0.060 & 0.156 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The probabilities of reduced scenarios in Case 1.  
Figure 8: Energy consumption load in Case 1: (**a**) electrical load, (**b**) thermal load.  
Figure 7: The reduced scenarios of total number of available EVs at each time instant in Case 1.