# Cooperative Multi-Objective Optimization of DC Multi-Microgrid Systems in Distribution Networks
## 3 Case 3
### Nomenclature
\begin{tabular}{l l} \(E_{C}\) & Total carbon emissions of MMGS and the distribution network. \\ \(E_{Cim}\) & Carbon emissions generated by \(m\)-th MG in the inner-loop model. \\ \(E_{CO}\) & Carbon emissions in the outer-loop model. \\ \(e_{c}\) & Carbon emissions factor. \\ \(f\) & The main objective function of the cooperative optimization model. \\ \(f_{1}\) & The objective functions of the inner-loop model. \\ \(f_{2}\) & The objective functions of the outer-loop model. \\ \(G_{ij}\) & Conductance of branch \(ij\) in the distribution network. \\ \(I_{ij}^{\max}\) & Upper limit of branch \(ij\) current carrying capacity in the distribution network. \\ \(i_{j}\) & Nodes of the distribution network. \\ \(k_{il}\) & Loss cost coefficient. \\ \(k_{c}\) & Carbon cost factor. \\ \(k_{cy}\) & Number of additional charging/discharging cycles. \\ \(k_{i}\) & The state variable of the \(i\)-th branch switch. \\ \(M\) & Number of MGs in the MMGS. \\ \(N\) & Number of EVs in \(m\)-th MG. \\ \(N_{\eta v}\) & Number of branches in the distribution network. \\ \(P_{\eta\mu}^{EV}\) & Exchanging power in the \(t\)-th hour of the \(n\)-th EV in the \(m\)-th MG. \\ \(P_{\eta\mu,t}^{EV}\) & Exchanging power in the \(t\)-th hour of the EVs in the \(m\)-th MG. \\ \(P_{\eta\mu,t}^{EV}\) & Power of the EVCDIs of the \(n\)-th EV in the \(m\)-th MG in the \(t\)-th hour. \\ \(P_{\mu,t}^{PV}\) & Power output of PVs in the \(m\)-th MG in the \(t\)-th hour. \\ \(P_{m,t}^{\Psi T}\) & power output of WTs in the \(m\)-th MG in the \(t\)-th hour. \\ \(P_{m,t}^{G}\) & Active power output between the \(m\)-th MG and the distribution network in the \\ \(P_{\eta\mu,t}^{EVCDIs}\) & \(t\)-th hour through the DC/AC converters. \\ \(P_{\eta\mu,t}^{PVCDIs}\) & Rated power of the EVCDI serving the \(n\)-th EV in the \(m\)-th MG. \\ \(P_{m,t}^{\Pi}\) & Total load of the \(m\)-th MG in the \(t\)-th hour. \\ \(P_{ij,t}^{\Pi}\) & Active power of branch \(ij\) in the \(t\)-th hour. \\ \(P_{ij,t}^{\Pi}\) & Initially active power of branch \(ij\) when connected without MG in the \(t\)-th hour. \\ \(P_{i,t}^{0}\) & Initial input active power of node \(i\) in the \(t\)-th hour. \\ \(P_{i,t}\) & Active load of node \(i\) in the \(t\)-th hour. \\ \(P_{ij,\max}\) & Maximum active power of the branch \(ij\). \\ \(Q_{ij,t}\) & Reactive power of branch \(ij\) in the \(t\)-th hour. \\ \(Q_{ij,t}^{0}\) & Initially reactive power of branch \(ij\) when connected without MMGS in the \(t\)-th hour. \\ \(Q_{m,t}^{G}\) & Reactive power output between the \(m\)-th MG and the distribution network in the \(t\)-th hour through the DC/AC converters. \\ \(Q_{i,t}^{0}\) & Initial input reactive power of node \(i\) in the \(t\)-th hour. \\ \(Q_{Li,t}\) & Reactive load of node \(i\) in the \(t\)-th hour. \\ \(Q_{ij,\max}\) & Maximum reactive power of the branch \(ij\). \\ \(R_{ij}\) & The resistance of branch \(ij\). \\ \(SOC_{EVm,\mu,t}\) & Remaining power capacity of the \(n\)-th EV in the \(m\)-th MG in the \(t\)-th hour. \\ \(SOC_{EVm,\mu,\min}\) & Minima capacity, respectively, of the \(n\)-th EV in the \(m\)-th MG. \\ \(SOC_{EVm,\mu,\max}\) & Maximum capacity, respectively, of the \(n\)-th EV in the \(m\)-th MG. \\ \(S_{m}\) & Rated power of the DC/AC converter in the \(m\)-th MG. \\ \(T\) & Scheduling cycle, one day, 24 h. \\ \(V_{ij,t}\) & Voltage of branch \(ij\) in the \(t\)-th hour. \\ \(V_{i}^{\min}\) & Lower limits of the node \(i\) voltage amplitude. \\ \(V_{i}^{\max}\) & Upper limits of the node \(i\) voltage amplitude. \\ \(W_{S}^{\emptyset}\) & Original baseline network loss. \\ \(W_{S}^{\emptyset\emptyset}\) & Total daily operating network loss of the distribution network. \\ \(W_{S}^{\emptyset}\) & Daily operating increased network loss of the distribution network. \\ \(\sigma\) & Self-discharge coefficient of EV's battery. \\ \(\Delta t\) & Length of the time slot set for the optimization. \\ \(\eta_{DEV}\) & Efficiency for EV discharging. \\ \(\eta_{CEV}\) & Efficiency for EV charging. \\ \(\delta_{ij}\) & Phase angle difference of branch \(ij\). \\ \end{tabular}