## 4 Case Studies
### Optimization Results
#### 4.1.2 Typical Winter Day  
The initial multi-energy load profiles for a typical winter day are shown by dashed lines in Figure 9(a). In this study, the heat is mainly used for the space heating and it is assumed that there are no cooling loads in winter. Available PV generation computed by p-efficient point at a confidence level of 0.85 is plotted by a blue dotted line in Figure 9(a). TOU electricity price curve is consistent with the curve shown in Figure 4. Natural gas price is a fixed price of 2.76V/m3. In Figure 9(a), the solid lines represent the optimized electrical, cooling and heating load profiles, respectively, considering IDR. The shift amount of the electrical and heat loads in the entire scheduling period is indicated in Figure 9(b). It shows that IDR transfers a certain amount of the electrical and heat loads from the peak periods, i.e., 8-12 and 17-20, to the valley period, i.e., 1-7, and off-peak periods, i.e., 12-17 and 20-24, to flatten the load curve, which leads to reduction of cost. Figure 11 shows a comparison in electricity purchased from the grid, gas purchased from the gas network and PV power utilization, respectively, under the proposed optimization framework with and without considering IDR. It is observed in Figure 11 that there is little difference in the amount of purchased gas due to a fixed gas price, and the amount of the purchased electricity in the valley periods is increased and at the peak periods is reduced to save cost. Electricity and gas resources are interdependent and complement each other, which enhances the flexibility of the MEMG system. The total cost of the purchased electricity and gas is attained as 1127V with considering IDR, which was 1168V without considering IDR. This represents a reduction of 3.5% in the energy purchasing cost. The optimized operation state of the energy conversion facilities over a 24-h period on an hourly basis is shown in Figure 12. Scheduling of the ES and HS and their SOC dynamics are shown in Figure 13. It is observed in Figure 12 that the CHP is committed  
Figure 9: Purchased energy and PV power accommodation on a typical summer day. during the entire scheduling period. The reason is that the CHP is the main heating unit to produce heat energy for supplying a large part of the total heat demand in the winter scenario. For the rest, the heat energy produced by the EHP and GB and stored heat energy in the HS are used to satisfy the remaining heat demand of the MEMG system. At the same time, electrical load demand is supplied by the main grid, electrical power produced by the CHP, available PV power and charging and discharging power of the ES. We can also learn from Figures 12 and 13 that during the valley period, i.e., 1-7, as the electricity price is low, providing a portion of the system heat demand by the EHP is more economical than by CHP, so that has cut down the heat energy produced by the CHP while increasing that produced by the EHP. During the peak periods, i.e., 8-12 and 17-20, as the electricity price is high, the production cost of heat generated from gas is more economical than that generated from electricity, so that has cut down the heat energy produced by the EHP while increasing that produced by the CHP. Meanwhile, the ES and HS capture the energy produced during the valley and off-peak periods, which is used to assist in the energy supply during the peak periods, e.g., 8-12 and 17-20, to save cost, which can be seen from Figure 13. All equipment operates in a coordinated manner to realize the energy efficiency optimization and economic system operation. Figure 11: Purchased energy and PV power accommodation on a typical winter day.