## 4 Case Studies
### Optimization Results  
#### 4.1.1 Typical Summer Day  
The initial daily electrical/cooling/heating load profiles for a typical summer day and time-of-use (TOU) electricity price are illustrated in Figure 4. PV generation obtained by the p-efficient point method based on historical data at different confidence levels is illustrated in Figure 5. In this set of tests, gas price is considered as a fixed price of 2.76\(\mathrm{\SIUnitSymbolMicro m^{3}}\), PV generation obtained by the p-efficient point method at confidence level 0.9 is used, and it is assumed that 10% of the initial electrical/cooling/heat load participates in IDR. This study solves the optimization problem over a 24-h period on an hourly basis. Time horizon is separated into three periods: peak periods from 8 to 12 and 17 to 20, off-peak periods from 12 to 17 and 20 to 24, and valley periods from 1 to 7. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline \(\eta_{E}^{CHP}/\eta_{H}^{CHP}\) & 0.35/0.45 & \(P_{Max}^{CHP}\) & 55 kW \\ \(\eta_{H}^{GB}\) & 0.85 & \(P_{Max}^{GB}\) & 20 kW \\ \(\zeta_{EHP}\) & 2.3 & \(P_{Max}^{\mathrm{EHP}}\) & 35 kW \\ \(\zeta_{EC}\) & 2.9 & \(P_{Max}^{EC}\) & 60 kW \\ \(\zeta_{AC}\) & 0.8 & \(P_{Max}^{\mathrm{AC}}\) & 20 kW \\ \(\eta_{B,ch}/\eta_{B,dis}\) & 0.9 & \(P_{B,ch}^{\mathrm{max}}/P_{B,dis}^{\mathrm{max}}\) & 20 kW \\ \(E_{B}^{\mathrm{min}}\) & 10 kWh & \(E_{B}^{max}\) & 90 kWh \\ \(\eta_{\phi,ch}/\eta_{\phi,dis}\) & 0.9 & \(P_{\phi,ch}^{\mathrm{max}}/P_{\phi,dis}^{\mathrm{max}}\) & 10 kW \\ \(E_{\phi}^{\mathrm{min}}\) & 0 & \(E_{\phi}^{\mathrm{max}}\) & 48 kWh \\ \(\kappa_{B}\) & 0.001 & \(\kappa_{\phi}\) & 0.001 \\ \hline \hline \end{tabular} _CHP:_ combined heat and power; _GB:_ gas boiler; _EHP_: electrical heat pump; _EC_: electric chiller; _AC_: absorption chiller; \(\eta_{L}^{CHP}/\eta_{H}^{CHP}\): electrical/heat conversion efficiency; \(\eta_{H}^{GB}\): conversion coefficient; \(\zeta\): coefficient of performance; \(P_{Max}^{\mathrm{max}}\): maximum power limit; \(\eta_{ch}/\eta_{dis}\): charging/discharging efficiency; _B_: battery; \(\varphi\): heat storage or cooling storage tank; \(E^{\mathrm{min}}/E^{\mathrm{max}}\): minimum and maximum energy stored in storage; \(P_{ch}^{\mathrm{max}}/P_{dis}^{\mathrm{max}}\): maximum charging/discharging power; \(\kappa\): decay rate of storage.  
\end{table} 
Table 1: The equipment parameters for the test system. Figure 3: Historical data of solar PV power used for the p-efficient point method: (**a**) the historical data for typical summer days; (**b**) the historical data for typical winter days. The optimized electrical, cooling and heating load profiles with and without considering IDR are comparatively studied in Figure 6a. The shift amount of electrical, cooling and heating loads in the entire scheduling period, i.e., a 24-h period on an hourly basis, is indicated in Figure 6b. Figure 4: Electrical/cooling/heating load profiles for a typical summer day and electrical price curve. Figure 5: PV generation profiles for a typical summer day obtained by the p-efficient point method at different confidence levels. Figure 6: Multi-energy load profiles before and after integrated demand response (IDR) implementation on a typical summer day, respectively: (**a**) comparison of electrical, cooling and heating load profiles before and after IDR, respectively; (**b**) electrical, cooling and heating load shift amount at different times of the day, where the negative value indicates the amount of energy demand reduction and the positive value indicates the amount of energy demand increment. As observed in Figure 6, after performing the proposed optimization model, the electrical, cooling and heating load demands of peak periods are reduced and a certain amount is shifted to the valley period, which adjusts the peak by filling the valley sag.