*2.1. Cost Functions*

The economic analysis in this work employs the *TIC*, the *TGC*, and the *PLC*. To calculate the *TIC*, maintenance, operation and installation costs are considered. For the *TGC*, reference bus active power generation cost (*PGC*), and DG units *PGC* and reactive power generation cost (*QGC*) are taken into account.

#### 2.1.1. Power Losses Cost

The *PLC* is determined by the continuation power flow using the mathematical formulation presented in [54].

$$PLC = \sum\_{p \le N\_p} \sum\_{ij \in \mathcal{N}\_\mathbb{L}} P l\_{ij,p} \cdot C\_{\mathbb{L},p} \cdot a\_p^{\text{PL.C}} \tag{1}$$

where *α*PLC *p* (Equation (2)) is the power loss discount rate for the *PLC* determination in period *p*; *Plij*,*<sup>p</sup>* are the power losses in the line *ij* in period *p*; *<sup>C</sup>*L,*p* is the cost of losses in period *p* in \$/kWh, *Np* is the period set and *NL* is the lines set.

The discount factors are determined by means of:

$$a\_p^{\rm PLC} = \sum\_{y=1}^{ny} \frac{\left(1 + LG\_p\right)^y}{(1+r)^{(ny)(p-1)+y}} \tag{2}$$

where *ny* are the periods in the planning horizon in years; *LGp* is the load annual growth rate in period *p*; and *r* is the annual interest rate.
