## Appendix A
### Nomenclature  
\begin{tabular}{l l} \(Nb\) & Number of system buses. \\ \(Ng\) & Number of generating units. \\ \(Nj\) & Set of loads number. \\ \(Ns\) & Number of scenarios. \\ \(Nw(Np)\) & Number of WT (PV) units. \\ \(Nk\) & Number of EVs. \\ \(T\) & Scheduling time (24 h a day). \\ \(i\) (\(j\)) & Index of generating units (loads), running from 1 to \(Ng(Nj)\). \\ \(b,n,r\) & Indices of system buses, running from 1 to \(Nb\). \\ \(t\) & Index of time periods, running from 1 to \(T\). \\ \(s\) & Index of scenarios, running from 1 to \(Ns\). \\ \(w\) (\(p\)) & Index of WT (PV) units, running from 1 to \(Nw(Np)\). \\ \(k\) & Index of EVs, running from 1 to \(Nk\). \\ \(v\) & Wind speed (m/s). \\ \(B(t)\) & Customer's benefit in period \(t\) (\$). \\ \(BPR_{t}(SPR_{t})\) & Electricity paying (selling) price for EVs charging (discharging) in period \(t\) (\$/kWh). \\ \(C_{p,t}(C_{p,t})\) & Energy bid submitted by WT \(w\) (PV \(p\)) in period \(t\) (\$/kWh). \\ \(C_{t}^{R^{U}}(C_{t}^{R^{U}})\) & Bid of the up (down) -spinning reserve submitted by unit \(i\) in period \(t\) (\$/kWh). \\ \(C_{t,t}^{RN}\) & Bid of the up (down) -spinning reserve submitted by load \(j\) in period \(t\) (\$/kWh). \\ \(D(t)\) & Power demand in period \(t\) (kW). \\ \(D_{DR}(t)\) & Power demand after implementing DR programs in period \(t\) (kW). \\ \(E(t,t)\) & Elasticity of load demand. \\ \(SUC_{i,t}(SDC_{i,t})\) & Start-up (Shut-down) cost of unit \(i\) in period \(t\) (\$). \\ \(\rho(t)\) & Electricity price in period \(t\) (\$/kW). \\ \(P_{i,t}(P_{i,t,s})\) & Scheduled power of unit \(i\) in period \(t\) (and scenario \(s\)) (kW). \\ \(P_{w,t}(P_{w,t,s})\) & Output power of WT \(w\) in period \(t\) (and scenario \(s\)) (kW). \\ \(P_{p,t}(P_{p,t,s})\) & Output power of PV \(p\) in period \(t\) (and scenario \(s\)) (kW). \\ \(P_{max}^{x}(P_{min})\) & Maximum (Minimum) generating capacity of unit \(x\) (kW). \\ \(P_{k,t}^{c}(P_{k,t}^{d})\) & Charging (Discharging) power of EV \(k\) in period \(t\) (kW). \\ \(P_{k,t}^{EV}\) & Power of EV \(k\) in period \(t\) (kW). \\ \(R_{t,t}^{U}(R_{t,t}^{U})\) & Scheduled up-spinning reserve for unit \(i\) (load \(j\)) in in period \(t\) (kW). \\ \(R_{t,t}^{D}(R_{t,t}^{D})\) & Scheduled down-spinning reserve for unit \(i\) (load \(j\)) in period \(t\) (kW). \\ \(R_{t,t}^{NS}\) & Scheduled non-spinning reserve for unit \(i\) in period \(t\) (kW). \\ \(r_{t,t,s}^{U}(r_{t,s}^{U})\) & Up-spinning reserve deployed by unit \(i\) (load \(j\)) in period \(t\) (and scenario \(s\)) (kW). \\ \(r_{t,s}^{D}(r_{t,s}^{D})\) & Down-spinning reserve deployed by unit \(i\) (load \(j\)) in period \(t\) (and scenario \(s\)) (kW). \\ \(S(t)\) & Customer's income at period \(t\) (\$). \\ \(V^{UOL}\) & Cost of involuntary load shedding for inelastic loads (\$/kWh). \\ \(L_{j,t}(L_{j,t,s})\) & Power scheduled for load \(j\) in period \(t\) (and scenario \(s\)) (kW). \\ \(L_{j,t}^{sheid}\) & Inelastic load shedding level of \(j^{th}\) load in period \(t\) and scenario \(s\) (kW). \\ \(F_{t,t}(F_{t,s})\) & Power flow through line \(l\) in period \(t\) (and scenario \(s\)) (kW). \\ \(\delta_{x,t}(\delta_{x,t,s})\) & Voltage angle at node \(x\) in period \(t\) (and scenario \(s\)) (radian). \\ \(\eta_{c}(\eta_{d})\) & Charging (Discharging) efficiency of EV \\ \(u_{i,t}(u_{i,t,s})\) & Binary variable, equal to 1 if unit \(i\) is scheduled to be committed in period \(t\) (and scenario \(s\)), otherwise 0. \\ \(y_{i,t}(y_{i,t,s})\) & Binary variable, equal to 1 if unit \(i\) is starting up in period \(t\) (and scenario \(s\)), otherwise 0. \\ \(z_{i,t}(z_{i,t,s})\) & Binary variable, equal to 1 if unit \(i\) is shut down in period \(t\) (and scenario \(s\)), otherwise 0. \\ \(x_{k,t}\) & Binary variable expressing the charging/discharging status of EV \(k\), equal to 1 if it is \\ \(x_{k,t}\) & Chargeing (Discharging) efficiency of EV \\ \(\rho(t)\) & Electricity price in period \(t\) (\$/kWh). \\ \(P_{i,t}(P_{i,t,s})\) & Scheduled power of unit \(i\) in period \(t\) (and scenario \(s\)) (kW).