*3.1. Objective Functions*

The major objective function of this work was to minimize several costs incurred in distribution networks (*C*system) consisting of voltage regulation cost (*C*VR), power loss cost (*C*Loss), and peak demand cost (*C*P) in terms of infrastructure development deferrals. Equation (10) represents the objective function and several costs can be found by Equations (11)–(14).

$$f(\mathbb{C}\_{i\bar{F}}) = \min \{ \mathbb{C}\_{\text{system}} \} \tag{10}$$

$$\mathcal{C}\_{\text{system}} = \mathcal{C}\_{\text{VR}} + \mathcal{C}\_{\text{Loss}} + \mathcal{C}\_{\text{P}} \tag{11}$$

$$\mathcal{C}\_{\rm VR} = (\sum\_{t=1}^{T} \sum\_{i=1}^{N} |V\_i - V\_{\rm ref}|) \times \gamma\_{\rm VR} \tag{12}$$

$$\mathcal{C}\_{\text{Loss}} = \left(\sum\_{t=1}^{T} \sum\_{i=1}^{M} (LineLoss) \times \gamma\_{\text{loss}}\right) \tag{13}$$

$$\mathbf{C}\_{\rm P} = P\_{\rm max} \times \Delta t \times \gamma\_{\rm P} \tag{14}$$

where *N*, *Vi*, *V*ref, *M*, *LineLoss*, *Pmax*, γVR, γloss, and γ<sup>P</sup> are total bus number, voltage magnitude (per unit) at the *i*th bus, reference voltage which is equal to 1 p.u., total branch number, active power loss in each

branch, maximum active power at slack bus over the considered period, rate of voltage regulation cost, rate of power loss cost, and rate of peak demand cost (γVR = 0.142 \$/p.u. [15], γloss = 0.284 \$/kWh [14], γ<sup>P</sup> = 200 \$/kWh/year [14]), respectively.
