2.1.2. FACTS Costs

In this research, HVDC, TCSC, SSSC, STATCOM, SVC and UPFC are the devices considered to enhance the power system network, and thus, it is necessary to determine the FACTS investment cost (*FIC*).

$$FIC = \sum\_{i \in N \models} \text{CRF} \cdot C\_i \tag{3}$$

where *N*F is the FACTS set, the FACTS cost (*Ci*) and the capital recovery factor (CRF) [27–29,55–63] are:

$$\mathbf{C}\_{i} = F\_{1,i} \cdot S\_{i}^{2} - F\_{2,i} \cdot S\_{i} + F\_{3,i} \tag{4}$$

$$\text{CRF} = \frac{r\left(1+r\right)^{ny}}{\left(1+r\right)^{ny}-1} \tag{5}$$

where *Si* is the nominal apparent power of FACTS *i*.

The values of the coefficients *<sup>F</sup>*1,*i*, *<sup>F</sup>*2,*i* and *<sup>F</sup>*3,*i* are specified in Table A1. These coefficients are retrieved from [18–25,64]. For the STATCOM function, the data curve recognition provided by [18] is employed; the values for the HVDC are obtained by adjusting the curve using the cost information calculated in [64].

#### 2.1.3. Distributed Generation Costs

The DG units are considered as PV nodes and the costs are simulated as diesel generators. In [30–32,36,65–67], the simplified equation for *PGC* is presented, taking into account the equations developed by [68].

$$PGC = 8760 \cdot \left\{ \left[ \sum\_{i \in N\_G} \left( a\_{2,i} \cdot P\_{\text{G,i}}^2 + a\_{1,i} \cdot P\_{\text{G,i}} + a\_{0,i} \right) \right] + 61.38 \cdot P\_{\text{G,SW}} \right\} \tag{6}$$

where *<sup>α</sup>*2,*i*, *<sup>α</sup>*1,*i* and *<sup>α</sup>*0,*i* are the generators coefficients [57,62,69–72] (Table A2); the coefficient 61.38 is obtained from [73]; *<sup>P</sup>*G,*i* is the active power supplied by generator *i* and *N*G is the generators set.

The *QGC* equations are developed in [65,74], where *β*1,*i* = 0.1*<sup>α</sup>*1,*i* and *β*0,*i* = 0.1*<sup>α</sup>*0,*i* [65]; and *Q*G,*i* is the reactive power supplied by generator *i*.

$$\text{QGC} = 8760 \cdot \left[ \sum\_{i \in N\_G} (\beta\_1 \cdot Q\_{G,i} + \beta\_0) \right] \tag{7}$$

The distributed generation investment cost (*GIC*) function considers the CRF, DG installation cost, and operation and maintenance costs in the *Ci* value [75].

$$IGC = \sum\_{i \in N\_G} \text{CRF} \cdot C\_i \tag{8}$$
