## Abbreviations
\begin{tabular}{l l} \(C^{opre}_{SOP}\) & the cost of SOP operation and maintenance \\ \(C^{res}_{ES}\) & the investment cost of energy storage \\ \(C^{res}_{ES}\) & the cost of energy storage operation and maintenance \\ \(C^{diss}_{loss}\) & the cost of power supply loss in the distribution network \\ \(d_{1}\) & the SOP investment discount rate \\ \(y_{1}\) & the service life of SOP \\ \(N_{SOP}\) & the number of SOP installations to be selected \\ \(c_{k,SOP}\) & the unit capacity investment cost of the \(k\)th SOP \\ \(S_{k,SOP}\) & the capacity of the \(k\)th SOP \\ \(\eta\) & the coefficient of operation and maintenance costs \\ \(d_{2}\) & the discount rate for energy storage investment \\ \(y_{2}\) & the service life of energy storage \\ \(N_{ES}\) & the number of energy storage installations to be selected \\ \(c_{k,ES}\) & the investment cost per unit capacity of the \(k\)th energy storage \\ \(S_{k,ES}\) & the capacity of the \(k\)th energy storage \\ \(c^{opre}_{k,ES}\) & the operating and maintenance cost of the \(k\)th energy storage unit's rated power \\ \(P_{k,ES}\) & the rated power of the \(k\)th energy storage; c is the electricity price \\ \(N_{t}\) & the total number of time periods \\ \(\Omega_{b}\) & the collection of all branches in the distribution system \\ \(r_{ij}\) & the resistance of the branch _ij_ \\ \(I_{ij,t}\) & the current amplitude of branch _ij_ during the \(t\)th time period \\ \(N_{i}\) & the total number of nodes in the distribution system \\ \(P^{loss}_{SOP,i,t}\) & the active power loss of SOP at node \(i\) during the \(t\)th time period \\ \(N_{s}\) & the total number of power nodes in the distribution system \\ \(P_{source,i,t}\) & the active power output of the \(i\)th power node during the \(t\)th time period \\ \(P_{source,ave}\) & the average active power output of all power nodes in the distribution system \\ \(x_{ij}\) & the reactance of branch _ij_ \\ \(P_{ij}\) & the active power flowing from node \(i\) to node \(j\) on the branch \\ \(Q_{ij}\) & the reactive power flowing from node \(i\) to node \(j\) on the branch \\ \(P_{i}\) & the sum of active power injected into node \(i\) \\ \(p^{ES}_{i}\) & the active power injected by the energy storage at node \(i\) \\ \(p^{SOP}_{i}\) & the active power injected by the SOP at node \(i\) \\ \(p^{LOAD}_{i}\) & the active power consumed by the load at node \(i\) \\ \(Q_{i}\) & the sum of the reactive power injected at node \(i\) \\ \(Q^{ES}_{i}\) & the reactive power injected by the energy storage at node \(i\) \\ \(Q^{SOP}_{i}\) & the reactive power injected by the SOP at node \(i\) \\ \(Q^{LOAD}_{i}\) & the reactive power consumed by the load at node \(i\) \\ \(\underline{U}\) & the minimum allowable node voltage values of the system \\ \(\overline{U}\) & the maximum allowable node voltage values of the system \\ \(\overline{I}\) & the maximum allowable branch current value of the system \\ \(P^{SOP,L}_{i}\) & the loss of SOP connected to node \(i\) \\ \(A^{SOP}_{i}\) & the loss coefficient of SOP connected to node \(i\) \\ \(S^{SOP}_{i}\) & the capacity of SOP connected to node \(i\) \\ \(P^{ES,\underline{c}}_{t}\) & the charging power of energy storage at time \(t\) \\ \(P^{ES,\underline{c}}_{t}\) & the discharging power of energy storage at time \(t\) \\ \(u^{ES,\underline{c}}_{t}\) & the charging states of energy storage at time \(t\) \\ \(u^{ES,\underline{c}}_{t}\) & the discharging states of energy storage at time \(t\) \\ \(p^{ES,\underline{\max}}\) & the maximum charging and discharging power of energy storage \\ \(SOC^{ES}_{t}\) & the state of charge of energy storage at time \(t\) \\ \(\eta_{c}\) & the charging efficiency of energy storage \\ \(\eta_{d}\) & the discharging efficiency of energy storage \\ \(SOC^{ES,\underline{\min}}\) & the minimum values of the energy storage state of charge \\ \(SOC^{ES,\underline{\max}}\) & the maximum values of the energy storage state of charge \\ \end{tabular}