## 3 Proposed Methodology
### Utilization of RES by the DSO  
The total daily demand by end users (2500 households) is assumed to be 50 MW. The energy usage data for a single household is obtained from taking the average daily consumption (per hour) per appliance for the house over a period of 1 month in winter. It is assumed that 20% of the total daily demand will be supplied by RES to compensate for demand during peak hours. Therefore, 5 MW is purchased from solar farms, while an additional 5 MW is supplied by a BESS installed by the DSO.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Appliance** & **Rating (KW)** & **Number** &
\begin{tabular}{c} **Operating** \\ **Time (h)** \\ \end{tabular} & \multirow{2}{*}{**Schedule**} & \multicolumn{2}{c}{**Energy Usage Sharing**} \\ \hline Geyser & 3.5 & 1 & & 06:00–07:00, & \multirow{2}{*}{Shiftable} & Smart plug \\ Electric kettle & 2.0 & 1 & 07:00–09:00 & & Shiftable & Smart plug \\ Toaster & 1.5 & 1 & 07:00–08:00 & & Shiftable & Smart plug \\ Microwave oven & 1.0 & 1 & 18:00–20:00 & & Shiftable & Smart plug \\ Dishwasher & 1.0 & 1 & 08:00–09:00, & \multirow{2}{*}{Shiftable} & Smart plug \\ Vacuum cleaner & 1.7 & 1 & 21:00–23:00 & & Shiftable & Smart plug \\ Electric iron & 1.2 & 1 & 06:00–07:00, & \multirow{2}{*}{Shiftable} & Smart plug \\ Washing machine & 0.33 & 1 & 22:00–00:00 & & Shiftable & Smart plug \\ TV & 0.065 & 1 & & 07:00–09:00, & \multirow{2}{*}{Shiftable} & Smart plug \\ Pool heater & 2.5 & 1 & 18:00–23:00 & & \\ Electric stove/oven & 4.0 & 1 & 07:00–08:00, & & Shiftable & Smart plug \\ Refrigerator & 0.25 & 1 & 00:00–00:00 & Non-shiftable & Smart plug \\ Lights & 0.024 & 10 & 06:00–08:00, & \multirow{2}{*}{Shiftable} & Zigbee enabled \\ Bedroom heater & 0.8 & 1 & 23:00–06:00 & & Shiftable & Smart plug \\ Miscellaneous loads & 1.0 & - & 07:00–09:00, & \multirow{2}{*}{Shiftable} & Smart plug \\  & & & 18:00–23:00 & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Appliance schedule for apartment [33].  
This paper does not consider the installation costs of the BESS in the cost analysis. The cost of electricity generated by the DSO is obtained according to:  
\[c_{g,t}=c_{g,t}(\mu_{nDR})+c_{g,t}(\mu_{sol})-c_{g,t}(\mu_{BESS}). \tag{4}\]  
From Equation (4), it is clear to see that utilization of RES is beneficial to the DSO since excess energy demand from non-participation in DR programs is obtained from the renewable energy sources. First priority for utilization of RES during peak hours is given to the BESS since the DSO does not pay for energy generated. In other words, the cost of energy purchased from solar farms remains zero until the combined capacities of the conventional grid and BESS are exceeded.  
With regard to the BESS, parameters specifying state-of-charge (SoC) of the battery bank are described in the following [34]:  
\[\omega_{t+1}=\frac{\omega_{t}+\eta_{c}p_{c,t}\cdot\phi_{t_{c}}}{\alpha_{c}}- \frac{p_{d,t}\cdot\phi_{t_{d}}}{\eta_{d}\cdot\alpha_{c}}-\beta_{d}\cdot\phi_{ sd}, \tag{5}\]  
\[0\leq p_{c,t}\leq p_{c,t,max}\cdot\delta_{c,t}\, \tag{6}\]  
\[0\leq p_{d,t}\leq p_{d,t,max}\cdot\delta_{d,t}\, \tag{7}\]  
\[\delta_{c,t}+\delta_{d,t}=1. \tag{8}\]  
The solar panel parameters are specified according to [35]:  
\[p_{sol}=V_{T_{s}}\cdot I_{S_{out}}\, \tag{9}\]  
\[V_{T_{s}}=\frac{n_{c}KT}{\varphi_{c}}, \tag{10}\]  
\[I_{S_{out}}=I_{r}-I_{sat,d}(e^{(\frac{V_{o}+I_{S}R_{S}}{\theta_{d}V_{T_{s}}})} -1)\ -(\frac{V_{o}+I_{S}R_{S}}{R_{r}}). \tag{11}\]