## 4 Simulation Results and Discussion  
### Test Case  
The simulations are performed over a modified residential MG which is presented in Figure 1 [30]. There are different types of distributed generation (DG) units in the MG including two micro-turbines (MT1 & MT2), two fuel cell (FC1 & FC2) units, and one gas engine (GE) unit. Also, there are a number of renewable-based prime movers in the system including three WTs, each with a capacity of 80 kW installed at bus 6, 9 and 16, respectively and two PV plants, each with a capacity of 70 kW installed at buses 5 and 10, respectively. The wind and PV power generation are a function of random wind speed and sun radiation, respectively. Their output power scenarios are reduced by applying a k-means  
In this study, it is assumed that the total signed contracts for participating customers in DR programs are equal to 40% of the total load during the scheduling period. The price elasticity of demand is shown in Table 2, which is adopted from [27] with some modification. It is also assumed that there are two PLs with 40 charging stations in buses 3 and 11. The arrival time of EVs is modeled with a Gaussian distribution with \(\mu=19\) and \(\delta^{2}=10\)[35]. Moreover, the EVs connected to the MG are assumed to be capable of providing slow, medium and fast charging modes [28; 36]. For the studied MG, energy prices at different tariffs (RTP, TOU and CPP) are also depicted in Figure 4.  
The optimization horizon is considered to be a day with 24 time intervals. To simulate the environmental/behavioral uncertainties within the system, 3000 scenarios are generated based on Weibull, Beta, and Gaussian PDFs to represent different values for wind speed, irradiation and EVs owners' behaviors, respectively. In the next step, the k-means algorithm is applied to reduce the generated scenarios to an optimal subset that represents well enough the uncertainties. The reduced scenarios are then applied to the proposed mixed integer programming (MIP)-based optimization stage to minimize the expected cost at scheduling time horizon. The effect of demand-side participation in different TBR-based DR programs in the MG energy and reserve scheduling is also analyzed. The optimization is carried out by CPLEX solver using GAMS software (Release 24.7.3 r58181 WEX-WEI  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Emission** & \(\mathbf{C^{R^{NS}}}\) & \(\mathbf{C^{R^{D}}}\) & \(\mathbf{C^{R^{U}}}\) & \(\mathbf{SDC}\) & \(\mathbf{SUC}\) & \(\mathbf{B\) (\$)} & \(\mathbf{A}\) & \(\mathbf{p^{max}}\) & \(\mathbf{p^{min}}\) & **DG** \\
**(kg/kWh)** & **(\$)** & **(\$)** & **(\$)** & **(\$)** & **(\$)** & **(\$)** & **(\$)** & **(\$/kWh)** & **(kW)** & **(kW)** & **(kW)** \\ \hline
0.550 & 0.019 & 0.020 & 0.021 & 0.080 & 0.090 & 0.043 & 0.851 & 150 & 25 & MT\({}_{1}\) \\
0.550 & 0.019 & 0.020 & 0.021 & 0.080 & 0.090 & 0.044 & 0.851 & 150 & 25 & MT\({}_{2}\) \\
0.377 & 0.015 & 0.015 & 0.015 & 0.090 & 0.160 & 0.028 & 2.552 & 100 & 20 & FC\({}_{1}\) \\
0.377 & 0.015 & 0.015 & 0.015 & 0.090 & 0.160 & 0.029 & 2.552 & 100 & 20 & FC\({}_{2}\) \\
0.890 & 0.017 & 0.017 & 0.017 & 0.080 & 0.120 & 0.031 & 2.120 & 150 & 35 & GE \\ - & - & - & - & - & 0.106 & 0 & 80 & 0 & WT \\ - & - & - & - & - & - & 0.548 & 0 & 70 & 0 & PV \\ \hline \hline \end{tabular}
\end{table}
Table 1: Technical specifications of the simulated microgrid (MG) components.  
Figure 4: Energy prices at different tariffs (RTP, TOU and CPP).  
x86 64 bit/MS Windows, TU Braunschweig, Braunschweig, Germany) [37] on a PC with 4 GB of RAM and Intel Core i7 @ 2.60 GHz processor (Intel, Santa Clara, CA, USA).