## Abbreviations  
The following abbreviations are used in this manuscript: \begin{tabular}{l l} \(F\) & Total cost per year ($/Year) \\ \(C_{p}\) & Cost of per unit active power loss per year ($/kW-Year) \\ \(C_{q}\) & Cost of per unit reactive power loss per year ($/kvar-Year) \\ \(C_{\mathbb{C}}\) & Purchasing and installation cost of capacitor installed ($/kvar) \\ \(p_{loss}^{Tot}\) & Total active power loss kW \\ \(Q_{loss}^{Tot}\) & Total reactive power loss kvar \\ \(Q_{\mathbb{C}}^{C}\) & Total injected reactive power (kvar) \\ \(Q_{\mathbb{C}q}\) & Reactive power injection at location \(q\) \\ \(N_{b}\) & Number of nodes in the system \\ \(N_{c}\) & Number of capacitors to be placed in system \\ \(N_{\mathbb{C}}^{max}\) & Maximum permissible number of capacitors to be placed in the system \\ \(n\) & Life expectancy of the capacitors \\ \(Q_{L}^{Tot}\) & Total required reactive power by load \\ \(V_{q}\) & Bus voltage at node \(q\) \\ \(V_{q}^{min}\) & Minimum voltage at node \(q\) \\ \(V_{q}^{max}\) & Maximum voltage at node \(q\) \\ \(Q_{\mathbb{C}q}\) & Reactive power injection at node \(q\) \\ \(Q_{\mathbb{C}q}^{min}\) & Minimum reactive power injection at node \(q\) \\ \(Q_{\mathbb{C}q}^{max}\) & Maximum reactive power injection at node \(q\) \\ \(P_{\mathbb{L}q}\) & Total active power loads beyond the bus \(q\) \\ \(Q_{\mathbb{L}q}\) & Total reactive power loads beyond bus \(q\) \\ \(P_{lossk}\) & Total active power loss in line \(k\) \\ \(Q_{lossk}\) & Total reactive power loss in line \(k\) \\ \(i_{k}\) & Total current flowing over the line \(k\) \\ \(R_{k}\) & Total resistance of the line \(k\) \\ \(X_{k}\) & Total reactance of the line \(k\) \\ \(X_{i}^{k}\) & Initial position of \(i^{th}\) particle in \(k^{th}\) iteration \\ \(Vel_{i}^{k}\) & Initial velocity of \(i^{th}\) particle in \(k^{th}\) iteration \\ \(Vel_{i}^{k+1}\) & Modified velocity of \(i^{th}\) particle in \(k+1^{th}\) iteration \\ \(X_{i}^{k+1}\) & Modified position of \(i^{th}\) particle in \(k+1^{th}\) iteration \\ \(P_{best}^{b}\) & Personal best position of the particle \\ \(G_{best}^{b}\) & Global best position of the particle \\ \(w\) & The inertia weight \\ \(c_{1}\) & Constant for acceleration \\ \(c_{2}\) & Constant for acceleration \\ \(r_{1}\) & Random numbers between 0 and 1 \\ \(r_{2}\) & Random numbers between 0 and 1 \\ \end{tabular}   
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